Interchange the variables.

Rewrite the equation as <math><mstyle displaystyle="true"><mfrac><mrow><msup><mrow><mi>y</mi></mrow><mrow><mn>2</mn></mrow></msup></mrow><mrow><mn>8</mn></mrow></mfrac><mo>+</mo><mfrac><mrow><mn>3</mn><msup><mrow><mi>y</mi></mrow><mrow><mn>2</mn></mrow></msup></mrow><mrow><mn>2</mn></mrow></mfrac><mo>+</mo><mfrac><mrow><mn>9</mn><mi>y</mi></mrow><mrow><mn>2</mn></mrow></mfrac><mo>=</mo><mi>x</mi></mstyle></math> .

Simplify <math><mstyle displaystyle="true"><mfrac><mrow><msup><mrow><mi>y</mi></mrow><mrow><mn>2</mn></mrow></msup></mrow><mrow><mn>8</mn></mrow></mfrac><mo>+</mo><mfrac><mrow><mn>3</mn><msup><mrow><mi>y</mi></mrow><mrow><mn>2</mn></mrow></msup></mrow><mrow><mn>2</mn></mrow></mfrac><mo>+</mo><mfrac><mrow><mn>9</mn><mi>y</mi></mrow><mrow><mn>2</mn></mrow></mfrac></mstyle></math> .

To write <math><mstyle displaystyle="true"><mfrac><mrow><mn>3</mn><msup><mrow><mi>y</mi></mrow><mrow><mn>2</mn></mrow></msup></mrow><mrow><mn>2</mn></mrow></mfrac></mstyle></math> as a fraction with a common denominator, multiply by <math><mstyle displaystyle="true"><mfrac><mrow><mn>4</mn></mrow><mrow><mn>4</mn></mrow></mfrac></mstyle></math> .

Write each expression with a common denominator of <math><mstyle displaystyle="true"><mn>8</mn></mstyle></math> , by multiplying each by an appropriate factor of <math><mstyle displaystyle="true"><mn>1</mn></mstyle></math> .

Multiply <math><mstyle displaystyle="true"><mfrac><mrow><mn>3</mn><msup><mrow><mi>y</mi></mrow><mrow><mn>2</mn></mrow></msup></mrow><mrow><mn>2</mn></mrow></mfrac></mstyle></math> and <math><mstyle displaystyle="true"><mfrac><mrow><mn>4</mn></mrow><mrow><mn>4</mn></mrow></mfrac></mstyle></math> .

Multiply <math><mstyle displaystyle="true"><mn>2</mn></mstyle></math> by <math><mstyle displaystyle="true"><mn>4</mn></mstyle></math> .

Combine the numerators over the common denominator.

Simplify each term.

Simplify the numerator.

Factor <math><mstyle displaystyle="true"><msup><mrow><mi>y</mi></mrow><mrow><mn>2</mn></mrow></msup></mstyle></math> out of <math><mstyle displaystyle="true"><msup><mrow><mi>y</mi></mrow><mrow><mn>2</mn></mrow></msup><mo>+</mo><mn>3</mn><msup><mrow><mi>y</mi></mrow><mrow><mn>2</mn></mrow></msup><mo>⋅</mo><mn>4</mn></mstyle></math> .

Multiply by <math><mstyle displaystyle="true"><mn>1</mn></mstyle></math> .

Factor <math><mstyle displaystyle="true"><msup><mrow><mi>y</mi></mrow><mrow><mn>2</mn></mrow></msup></mstyle></math> out of <math><mstyle displaystyle="true"><mn>3</mn><msup><mrow><mi>y</mi></mrow><mrow><mn>2</mn></mrow></msup><mo>⋅</mo><mn>4</mn></mstyle></math> .

Factor <math><mstyle displaystyle="true"><msup><mrow><mi>y</mi></mrow><mrow><mn>2</mn></mrow></msup></mstyle></math> out of <math><mstyle displaystyle="true"><msup><mrow><mi>y</mi></mrow><mrow><mn>2</mn></mrow></msup><mo>⋅</mo><mn>1</mn><mo>+</mo><msup><mrow><mi>y</mi></mrow><mrow><mn>2</mn></mrow></msup><mrow><mo>(</mo><mn>3</mn><mo>⋅</mo><mn>4</mn><mo>)</mo></mrow></mstyle></math> .

Multiply <math><mstyle displaystyle="true"><mn>3</mn></mstyle></math> by <math><mstyle displaystyle="true"><mn>4</mn></mstyle></math> .

Add <math><mstyle displaystyle="true"><mn>1</mn></mstyle></math> and <math><mstyle displaystyle="true"><mn>12</mn></mstyle></math> .

Move <math><mstyle displaystyle="true"><mn>13</mn></mstyle></math> to the left of <math><mstyle displaystyle="true"><msup><mrow><mi>y</mi></mrow><mrow><mn>2</mn></mrow></msup></mstyle></math> .

Move <math><mstyle displaystyle="true"><mi>x</mi></mstyle></math> to the left side of the equation by subtracting it from both sides.

Multiply through by the least common denominator <math><mstyle displaystyle="true"><mn>8</mn></mstyle></math> , then simplify.

Apply the distributive property.

Simplify.

Cancel the common factor of <math><mstyle displaystyle="true"><mn>8</mn></mstyle></math> .

Cancel the common factor.

Rewrite the expression.

Cancel the common factor of <math><mstyle displaystyle="true"><mn>2</mn></mstyle></math> .

Factor <math><mstyle displaystyle="true"><mn>2</mn></mstyle></math> out of <math><mstyle displaystyle="true"><mn>8</mn></mstyle></math> .

Cancel the common factor.

Rewrite the expression.

Multiply <math><mstyle displaystyle="true"><mn>9</mn></mstyle></math> by <math><mstyle displaystyle="true"><mn>4</mn></mstyle></math> .

Multiply <math><mstyle displaystyle="true"><mo>-</mo><mn>1</mn></mstyle></math> by <math><mstyle displaystyle="true"><mn>8</mn></mstyle></math> .

Move <math><mstyle displaystyle="true"><mn>36</mn><mi>y</mi></mstyle></math> .

Use the quadratic formula to find the solutions.

Substitute the values <math><mstyle displaystyle="true"><mi>a</mi><mo>=</mo><mn>13</mn></mstyle></math> , <math><mstyle displaystyle="true"><mi>b</mi><mo>=</mo><mn>36</mn></mstyle></math> , and <math><mstyle displaystyle="true"><mi>c</mi><mo>=</mo><mo>-</mo><mn>8</mn><mi>x</mi></mstyle></math> into the quadratic formula and solve for <math><mstyle displaystyle="true"><mi>y</mi></mstyle></math> .

Simplify.

Simplify the numerator.

Raise <math><mstyle displaystyle="true"><mn>36</mn></mstyle></math> to the power of <math><mstyle displaystyle="true"><mn>2</mn></mstyle></math> .

Multiply <math><mstyle displaystyle="true"><mo>-</mo><mn>8</mn></mstyle></math> by <math><mstyle displaystyle="true"><mn>13</mn></mstyle></math> .

Multiply <math><mstyle displaystyle="true"><mo>-</mo><mn>104</mn></mstyle></math> by <math><mstyle displaystyle="true"><mo>-</mo><mn>4</mn></mstyle></math> .

Factor <math><mstyle displaystyle="true"><mn>16</mn></mstyle></math> out of <math><mstyle displaystyle="true"><mn>1296</mn><mo>+</mo><mn>416</mn><mi>x</mi></mstyle></math> .

Factor <math><mstyle displaystyle="true"><mn>16</mn></mstyle></math> out of <math><mstyle displaystyle="true"><mn>1296</mn></mstyle></math> .

Factor <math><mstyle displaystyle="true"><mn>16</mn></mstyle></math> out of <math><mstyle displaystyle="true"><mn>416</mn><mi>x</mi></mstyle></math> .

Factor <math><mstyle displaystyle="true"><mn>16</mn></mstyle></math> out of <math><mstyle displaystyle="true"><mn>16</mn><mrow><mo>(</mo><mn>81</mn><mo>)</mo></mrow><mo>+</mo><mn>16</mn><mrow><mo>(</mo><mn>26</mn><mi>x</mi><mo>)</mo></mrow></mstyle></math> .

Rewrite <math><mstyle displaystyle="true"><mn>16</mn><mrow><mo>(</mo><mn>81</mn><mo>+</mo><mn>26</mn><mi>x</mi><mo>)</mo></mrow></mstyle></math> as <math><mstyle displaystyle="true"><msup><mrow><mo>(</mo><msup><mrow><mn>2</mn></mrow><mrow><mn>2</mn></mrow></msup><mo>)</mo></mrow><mrow><mn>2</mn></mrow></msup><mrow><mo>(</mo><mn>81</mn><mo>+</mo><mn>26</mn><mi>x</mi><mo>)</mo></mrow></mstyle></math> .

Rewrite <math><mstyle displaystyle="true"><mn>16</mn></mstyle></math> as <math><mstyle displaystyle="true"><msup><mrow><mn>4</mn></mrow><mrow><mn>2</mn></mrow></msup></mstyle></math> .

Rewrite <math><mstyle displaystyle="true"><mn>4</mn></mstyle></math> as <math><mstyle displaystyle="true"><msup><mrow><mn>2</mn></mrow><mrow><mn>2</mn></mrow></msup></mstyle></math> .

Pull terms out from under the radical.

Raise <math><mstyle displaystyle="true"><mn>2</mn></mstyle></math> to the power of <math><mstyle displaystyle="true"><mn>2</mn></mstyle></math> .

Multiply <math><mstyle displaystyle="true"><mn>2</mn></mstyle></math> by <math><mstyle displaystyle="true"><mn>13</mn></mstyle></math> .

Simplify <math><mstyle displaystyle="true"><mfrac><mrow><mo>-</mo><mn>36</mn><mo>±</mo><mn>4</mn><msqrt><mn>81</mn><mo>+</mo><mn>26</mn><mi>x</mi></msqrt></mrow><mrow><mn>26</mn></mrow></mfrac></mstyle></math> .

Simplify the expression to solve for the <math><mstyle displaystyle="true"><mo>+</mo></mstyle></math> portion of the <math><mstyle displaystyle="true"><mo>±</mo></mstyle></math> .

Simplify the numerator.

Raise <math><mstyle displaystyle="true"><mn>36</mn></mstyle></math> to the power of <math><mstyle displaystyle="true"><mn>2</mn></mstyle></math> .

Multiply <math><mstyle displaystyle="true"><mo>-</mo><mn>8</mn></mstyle></math> by <math><mstyle displaystyle="true"><mn>13</mn></mstyle></math> .

Multiply <math><mstyle displaystyle="true"><mo>-</mo><mn>104</mn></mstyle></math> by <math><mstyle displaystyle="true"><mo>-</mo><mn>4</mn></mstyle></math> .

Factor <math><mstyle displaystyle="true"><mn>16</mn></mstyle></math> out of <math><mstyle displaystyle="true"><mn>1296</mn><mo>+</mo><mn>416</mn><mi>x</mi></mstyle></math> .

Factor <math><mstyle displaystyle="true"><mn>16</mn></mstyle></math> out of <math><mstyle displaystyle="true"><mn>1296</mn></mstyle></math> .

Factor <math><mstyle displaystyle="true"><mn>16</mn></mstyle></math> out of <math><mstyle displaystyle="true"><mn>416</mn><mi>x</mi></mstyle></math> .

Factor <math><mstyle displaystyle="true"><mn>16</mn></mstyle></math> out of <math><mstyle displaystyle="true"><mn>16</mn><mrow><mo>(</mo><mn>81</mn><mo>)</mo></mrow><mo>+</mo><mn>16</mn><mrow><mo>(</mo><mn>26</mn><mi>x</mi><mo>)</mo></mrow></mstyle></math> .

Rewrite <math><mstyle displaystyle="true"><mn>16</mn><mrow><mo>(</mo><mn>81</mn><mo>+</mo><mn>26</mn><mi>x</mi><mo>)</mo></mrow></mstyle></math> as <math><mstyle displaystyle="true"><msup><mrow><mo>(</mo><msup><mrow><mn>2</mn></mrow><mrow><mn>2</mn></mrow></msup><mo>)</mo></mrow><mrow><mn>2</mn></mrow></msup><mrow><mo>(</mo><mn>81</mn><mo>+</mo><mn>26</mn><mi>x</mi><mo>)</mo></mrow></mstyle></math> .

Rewrite <math><mstyle displaystyle="true"><mn>16</mn></mstyle></math> as <math><mstyle displaystyle="true"><msup><mrow><mn>4</mn></mrow><mrow><mn>2</mn></mrow></msup></mstyle></math> .

Rewrite <math><mstyle displaystyle="true"><mn>4</mn></mstyle></math> as <math><mstyle displaystyle="true"><msup><mrow><mn>2</mn></mrow><mrow><mn>2</mn></mrow></msup></mstyle></math> .

Pull terms out from under the radical.

Raise <math><mstyle displaystyle="true"><mn>2</mn></mstyle></math> to the power of <math><mstyle displaystyle="true"><mn>2</mn></mstyle></math> .

Multiply <math><mstyle displaystyle="true"><mn>2</mn></mstyle></math> by <math><mstyle displaystyle="true"><mn>13</mn></mstyle></math> .

Simplify <math><mstyle displaystyle="true"><mfrac><mrow><mo>-</mo><mn>36</mn><mo>±</mo><mn>4</mn><msqrt><mn>81</mn><mo>+</mo><mn>26</mn><mi>x</mi></msqrt></mrow><mrow><mn>26</mn></mrow></mfrac></mstyle></math> .

Change the <math><mstyle displaystyle="true"><mo>±</mo></mstyle></math> to <math><mstyle displaystyle="true"><mo>+</mo></mstyle></math> .

Factor <math><mstyle displaystyle="true"><mn>2</mn></mstyle></math> out of <math><mstyle displaystyle="true"><mo>-</mo><mn>18</mn><mo>+</mo><mn>2</mn><msqrt><mn>81</mn><mo>+</mo><mn>26</mn><mi>x</mi></msqrt></mstyle></math> .

Factor <math><mstyle displaystyle="true"><mn>2</mn></mstyle></math> out of <math><mstyle displaystyle="true"><mo>-</mo><mn>18</mn></mstyle></math> .

Factor <math><mstyle displaystyle="true"><mn>2</mn></mstyle></math> out of <math><mstyle displaystyle="true"><mn>2</mn><mo>⋅</mo><mo>-</mo><mn>9</mn><mo>+</mo><mn>2</mn><msqrt><mn>81</mn><mo>+</mo><mn>26</mn><mi>x</mi></msqrt></mstyle></math> .

Rewrite <math><mstyle displaystyle="true"><mo>-</mo><mn>9</mn></mstyle></math> as <math><mstyle displaystyle="true"><mo>-</mo><mn>1</mn><mrow><mo>(</mo><mn>9</mn><mo>)</mo></mrow></mstyle></math> .

Factor <math><mstyle displaystyle="true"><mo>-</mo><mn>1</mn></mstyle></math> out of <math><mstyle displaystyle="true"><msqrt><mn>81</mn><mo>+</mo><mn>26</mn><mi>x</mi></msqrt></mstyle></math> .

Factor <math><mstyle displaystyle="true"><mo>-</mo><mn>1</mn></mstyle></math> out of <math><mstyle displaystyle="true"><mo>-</mo><mn>1</mn><mrow><mo>(</mo><mn>9</mn><mo>)</mo></mrow><mo>-</mo><mn>1</mn><mrow><mo>(</mo><mo>-</mo><msqrt><mn>81</mn><mo>+</mo><mn>26</mn><mi>x</mi></msqrt><mo>)</mo></mrow></mstyle></math> .

Move the negative in front of the fraction.

Simplify the expression to solve for the <math><mstyle displaystyle="true"><mo>-</mo></mstyle></math> portion of the <math><mstyle displaystyle="true"><mo>±</mo></mstyle></math> .

Simplify the numerator.

Raise <math><mstyle displaystyle="true"><mn>36</mn></mstyle></math> to the power of <math><mstyle displaystyle="true"><mn>2</mn></mstyle></math> .

Multiply <math><mstyle displaystyle="true"><mo>-</mo><mn>8</mn></mstyle></math> by <math><mstyle displaystyle="true"><mn>13</mn></mstyle></math> .

Multiply <math><mstyle displaystyle="true"><mo>-</mo><mn>104</mn></mstyle></math> by <math><mstyle displaystyle="true"><mo>-</mo><mn>4</mn></mstyle></math> .

Factor <math><mstyle displaystyle="true"><mn>16</mn></mstyle></math> out of <math><mstyle displaystyle="true"><mn>1296</mn><mo>+</mo><mn>416</mn><mi>x</mi></mstyle></math> .

Factor <math><mstyle displaystyle="true"><mn>16</mn></mstyle></math> out of <math><mstyle displaystyle="true"><mn>1296</mn></mstyle></math> .

Factor <math><mstyle displaystyle="true"><mn>16</mn></mstyle></math> out of <math><mstyle displaystyle="true"><mn>416</mn><mi>x</mi></mstyle></math> .

Factor <math><mstyle displaystyle="true"><mn>16</mn></mstyle></math> out of <math><mstyle displaystyle="true"><mn>16</mn><mrow><mo>(</mo><mn>81</mn><mo>)</mo></mrow><mo>+</mo><mn>16</mn><mrow><mo>(</mo><mn>26</mn><mi>x</mi><mo>)</mo></mrow></mstyle></math> .

Rewrite <math><mstyle displaystyle="true"><mn>16</mn><mrow><mo>(</mo><mn>81</mn><mo>+</mo><mn>26</mn><mi>x</mi><mo>)</mo></mrow></mstyle></math> as <math><mstyle displaystyle="true"><msup><mrow><mo>(</mo><msup><mrow><mn>2</mn></mrow><mrow><mn>2</mn></mrow></msup><mo>)</mo></mrow><mrow><mn>2</mn></mrow></msup><mrow><mo>(</mo><mn>81</mn><mo>+</mo><mn>26</mn><mi>x</mi><mo>)</mo></mrow></mstyle></math> .

Rewrite <math><mstyle displaystyle="true"><mn>16</mn></mstyle></math> as <math><mstyle displaystyle="true"><msup><mrow><mn>4</mn></mrow><mrow><mn>2</mn></mrow></msup></mstyle></math> .

Rewrite <math><mstyle displaystyle="true"><mn>4</mn></mstyle></math> as <math><mstyle displaystyle="true"><msup><mrow><mn>2</mn></mrow><mrow><mn>2</mn></mrow></msup></mstyle></math> .

Pull terms out from under the radical.

Raise <math><mstyle displaystyle="true"><mn>2</mn></mstyle></math> to the power of <math><mstyle displaystyle="true"><mn>2</mn></mstyle></math> .

Multiply <math><mstyle displaystyle="true"><mn>2</mn></mstyle></math> by <math><mstyle displaystyle="true"><mn>13</mn></mstyle></math> .

Simplify <math><mstyle displaystyle="true"><mfrac><mrow><mo>-</mo><mn>36</mn><mo>±</mo><mn>4</mn><msqrt><mn>81</mn><mo>+</mo><mn>26</mn><mi>x</mi></msqrt></mrow><mrow><mn>26</mn></mrow></mfrac></mstyle></math> .

Change the <math><mstyle displaystyle="true"><mo>±</mo></mstyle></math> to <math><mstyle displaystyle="true"><mo>-</mo></mstyle></math> .

Factor <math><mstyle displaystyle="true"><mo>-</mo><mn>2</mn></mstyle></math> out of <math><mstyle displaystyle="true"><mo>-</mo><mn>18</mn><mo>-</mo><mn>2</mn><msqrt><mn>81</mn><mo>+</mo><mn>26</mn><mi>x</mi></msqrt></mstyle></math> .

Reorder <math><mstyle displaystyle="true"><mn>81</mn></mstyle></math> and <math><mstyle displaystyle="true"><mn>26</mn><mi>x</mi></mstyle></math> .

Factor <math><mstyle displaystyle="true"><mo>-</mo><mn>2</mn></mstyle></math> out of <math><mstyle displaystyle="true"><mo>-</mo><mn>18</mn></mstyle></math> .

Factor <math><mstyle displaystyle="true"><mo>-</mo><mn>2</mn></mstyle></math> out of <math><mstyle displaystyle="true"><mo>-</mo><mn>2</mn><msqrt><mn>26</mn><mi>x</mi><mo>+</mo><mn>81</mn></msqrt></mstyle></math> .

Factor <math><mstyle displaystyle="true"><mo>-</mo><mn>2</mn></mstyle></math> out of <math><mstyle displaystyle="true"><mo>-</mo><mn>2</mn><mrow><mo>(</mo><mn>9</mn><mo>)</mo></mrow><mo>-</mo><mn>2</mn><mrow><mo>(</mo><msqrt><mn>26</mn><mi>x</mi><mo>+</mo><mn>81</mn></msqrt><mo>)</mo></mrow></mstyle></math> .

Move the negative in front of the fraction.

The final answer is the combination of both solutions.

Replace the <math><mstyle displaystyle="true"><mi>y</mi></mstyle></math> with <math><mstyle displaystyle="true"><msup><mrow><mi>f</mi></mrow><mrow><mo>-</mo><mn>1</mn></mrow></msup><mrow><mo>(</mo><mi>x</mi><mo>)</mo></mrow></mstyle></math> to show the final answer.

Set up the composite result function.

Evaluate <math><mstyle displaystyle="true"><mi>g</mi><mrow><mo>(</mo><mi>f</mi><mrow><mo>(</mo><mi>x</mi><mo>)</mo></mrow><mo>)</mo></mrow></mstyle></math> by substituting in the value of <math><mstyle displaystyle="true"><mi>f</mi></mstyle></math> into <math><mstyle displaystyle="true"><mi>g</mi></mstyle></math> .

Simplify the numerator.

To write <math><mstyle displaystyle="true"><mfrac><mrow><mn>3</mn><msup><mrow><mi>x</mi></mrow><mrow><mn>2</mn></mrow></msup></mrow><mrow><mn>2</mn></mrow></mfrac></mstyle></math> as a fraction with a common denominator, multiply by <math><mstyle displaystyle="true"><mfrac><mrow><mn>4</mn></mrow><mrow><mn>4</mn></mrow></mfrac></mstyle></math> .

Write each expression with a common denominator of <math><mstyle displaystyle="true"><mn>8</mn></mstyle></math> , by multiplying each by an appropriate factor of <math><mstyle displaystyle="true"><mn>1</mn></mstyle></math> .

Multiply <math><mstyle displaystyle="true"><mfrac><mrow><mn>3</mn><msup><mrow><mi>x</mi></mrow><mrow><mn>2</mn></mrow></msup></mrow><mrow><mn>2</mn></mrow></mfrac></mstyle></math> and <math><mstyle displaystyle="true"><mfrac><mrow><mn>4</mn></mrow><mrow><mn>4</mn></mrow></mfrac></mstyle></math> .

Multiply <math><mstyle displaystyle="true"><mn>2</mn></mstyle></math> by <math><mstyle displaystyle="true"><mn>4</mn></mstyle></math> .

Combine the numerators over the common denominator.

Simplify each term.

Simplify the numerator.

Factor <math><mstyle displaystyle="true"><msup><mrow><mi>x</mi></mrow><mrow><mn>2</mn></mrow></msup></mstyle></math> out of <math><mstyle displaystyle="true"><msup><mrow><mi>x</mi></mrow><mrow><mn>2</mn></mrow></msup><mo>+</mo><mn>3</mn><msup><mrow><mi>x</mi></mrow><mrow><mn>2</mn></mrow></msup><mo>⋅</mo><mn>4</mn></mstyle></math> .

Multiply by <math><mstyle displaystyle="true"><mn>1</mn></mstyle></math> .

Factor <math><mstyle displaystyle="true"><msup><mrow><mi>x</mi></mrow><mrow><mn>2</mn></mrow></msup></mstyle></math> out of <math><mstyle displaystyle="true"><mn>3</mn><msup><mrow><mi>x</mi></mrow><mrow><mn>2</mn></mrow></msup><mo>⋅</mo><mn>4</mn></mstyle></math> .

Factor <math><mstyle displaystyle="true"><msup><mrow><mi>x</mi></mrow><mrow><mn>2</mn></mrow></msup></mstyle></math> out of <math><mstyle displaystyle="true"><msup><mrow><mi>x</mi></mrow><mrow><mn>2</mn></mrow></msup><mo>⋅</mo><mn>1</mn><mo>+</mo><msup><mrow><mi>x</mi></mrow><mrow><mn>2</mn></mrow></msup><mrow><mo>(</mo><mn>3</mn><mo>⋅</mo><mn>4</mn><mo>)</mo></mrow></mstyle></math> .

Multiply <math><mstyle displaystyle="true"><mn>3</mn></mstyle></math> by <math><mstyle displaystyle="true"><mn>4</mn></mstyle></math> .

Add <math><mstyle displaystyle="true"><mn>1</mn></mstyle></math> and <math><mstyle displaystyle="true"><mn>12</mn></mstyle></math> .

Move <math><mstyle displaystyle="true"><mn>13</mn></mstyle></math> to the left of <math><mstyle displaystyle="true"><msup><mrow><mi>x</mi></mrow><mrow><mn>2</mn></mrow></msup></mstyle></math> .

Apply the distributive property.

Cancel the common factor of <math><mstyle displaystyle="true"><mn>2</mn></mstyle></math> .

Factor <math><mstyle displaystyle="true"><mn>2</mn></mstyle></math> out of <math><mstyle displaystyle="true"><mn>26</mn></mstyle></math> .

Factor <math><mstyle displaystyle="true"><mn>2</mn></mstyle></math> out of <math><mstyle displaystyle="true"><mn>8</mn></mstyle></math> .

Cancel the common factor.

Rewrite the expression.

Combine <math><mstyle displaystyle="true"><mn>13</mn></mstyle></math> and <math><mstyle displaystyle="true"><mfrac><mrow><mn>13</mn><msup><mrow><mi>x</mi></mrow><mrow><mn>2</mn></mrow></msup></mrow><mrow><mn>4</mn></mrow></mfrac></mstyle></math> .

Multiply <math><mstyle displaystyle="true"><mn>13</mn></mstyle></math> by <math><mstyle displaystyle="true"><mn>13</mn></mstyle></math> .

Cancel the common factor of <math><mstyle displaystyle="true"><mn>2</mn></mstyle></math> .

Factor <math><mstyle displaystyle="true"><mn>2</mn></mstyle></math> out of <math><mstyle displaystyle="true"><mn>26</mn></mstyle></math> .

Cancel the common factor.

Rewrite the expression.

Multiply <math><mstyle displaystyle="true"><mn>9</mn></mstyle></math> by <math><mstyle displaystyle="true"><mn>13</mn></mstyle></math> .

Reorder terms.

Factor using the perfect square rule.

Rewrite <math><mstyle displaystyle="true"><mn>169</mn><msup><mrow><mi>x</mi></mrow><mrow><mn>2</mn></mrow></msup></mstyle></math> as <math><mstyle displaystyle="true"><msup><mrow><mo>(</mo><mn>13</mn><mi>x</mi><mo>)</mo></mrow><mrow><mn>2</mn></mrow></msup></mstyle></math> .

Rewrite <math><mstyle displaystyle="true"><mfrac><mrow><msup><mrow><mo>(</mo><mn>13</mn><mi>x</mi><mo>)</mo></mrow><mrow><mn>2</mn></mrow></msup></mrow><mrow><msup><mrow><mn>2</mn></mrow><mrow><mn>2</mn></mrow></msup></mrow></mfrac></mstyle></math> as <math><mstyle displaystyle="true"><msup><mrow><mo>(</mo><mfrac><mrow><mn>13</mn><mi>x</mi></mrow><mrow><mn>2</mn></mrow></mfrac><mo>)</mo></mrow><mrow><mn>2</mn></mrow></msup></mstyle></math> .

Rewrite <math><mstyle displaystyle="true"><mn>81</mn></mstyle></math> as <math><mstyle displaystyle="true"><msup><mrow><mn>9</mn></mrow><mrow><mn>2</mn></mrow></msup></mstyle></math> .

Check the middle term by multiplying <math><mstyle displaystyle="true"><mn>2</mn><mi>a</mi><mi>b</mi></mstyle></math> and compare this result with the middle term in the original expression.

Simplify.

Factor using the perfect square trinomial rule <math><mstyle displaystyle="true"><msup><mrow><mi>a</mi></mrow><mrow><mn>2</mn></mrow></msup><mo>+</mo><mn>2</mn><mi>a</mi><mi>b</mi><mo>+</mo><msup><mrow><mi>b</mi></mrow><mrow><mn>2</mn></mrow></msup><mo>=</mo><msup><mrow><mo>(</mo><mi>a</mi><mo>+</mo><mi>b</mi><mo>)</mo></mrow><mrow><mn>2</mn></mrow></msup></mstyle></math> , where <math><mstyle displaystyle="true"><mi>a</mi><mo>=</mo><mfrac><mrow><mn>13</mn><mi>x</mi></mrow><mrow><mn>2</mn></mrow></mfrac></mstyle></math> and <math><mstyle displaystyle="true"><mi>b</mi><mo>=</mo><mn>9</mn></mstyle></math> .

To write <math><mstyle displaystyle="true"><mn>9</mn></mstyle></math> as a fraction with a common denominator, multiply by <math><mstyle displaystyle="true"><mfrac><mrow><mn>2</mn></mrow><mrow><mn>2</mn></mrow></mfrac></mstyle></math> .

Combine <math><mstyle displaystyle="true"><mn>9</mn></mstyle></math> and <math><mstyle displaystyle="true"><mfrac><mrow><mn>2</mn></mrow><mrow><mn>2</mn></mrow></mfrac></mstyle></math> .

Combine the numerators over the common denominator.

Multiply <math><mstyle displaystyle="true"><mn>9</mn></mstyle></math> by <math><mstyle displaystyle="true"><mn>2</mn></mstyle></math> .

Apply the product rule to <math><mstyle displaystyle="true"><mfrac><mrow><mn>13</mn><mi>x</mi><mo>+</mo><mn>18</mn></mrow><mrow><mn>2</mn></mrow></mfrac></mstyle></math> .

Rewrite <math><mstyle displaystyle="true"><mfrac><mrow><msup><mrow><mo>(</mo><mn>13</mn><mi>x</mi><mo>+</mo><mn>18</mn><mo>)</mo></mrow><mrow><mn>2</mn></mrow></msup></mrow><mrow><msup><mrow><mn>2</mn></mrow><mrow><mn>2</mn></mrow></msup></mrow></mfrac></mstyle></math> as <math><mstyle displaystyle="true"><msup><mrow><mo>(</mo><mfrac><mrow><mn>13</mn><mi>x</mi><mo>+</mo><mn>18</mn></mrow><mrow><mn>2</mn></mrow></mfrac><mo>)</mo></mrow><mrow><mn>2</mn></mrow></msup></mstyle></math> .

Pull terms out from under the radical, assuming positive real numbers.

To write <math><mstyle displaystyle="true"><mn>9</mn></mstyle></math> as a fraction with a common denominator, multiply by <math><mstyle displaystyle="true"><mfrac><mrow><mn>2</mn></mrow><mrow><mn>2</mn></mrow></mfrac></mstyle></math> .

Combine <math><mstyle displaystyle="true"><mn>9</mn></mstyle></math> and <math><mstyle displaystyle="true"><mfrac><mrow><mn>2</mn></mrow><mrow><mn>2</mn></mrow></mfrac></mstyle></math> .

Combine the numerators over the common denominator.

Rewrite <math><mstyle displaystyle="true"><mfrac><mrow><mn>9</mn><mo>⋅</mo><mn>2</mn><mo>-</mo><mrow><mo>(</mo><mn>13</mn><mi>x</mi><mo>+</mo><mn>18</mn><mo>)</mo></mrow></mrow><mrow><mn>2</mn></mrow></mfrac></mstyle></math> in a factored form.

Multiply <math><mstyle displaystyle="true"><mn>9</mn></mstyle></math> by <math><mstyle displaystyle="true"><mn>2</mn></mstyle></math> .

Apply the distributive property.

Multiply <math><mstyle displaystyle="true"><mn>13</mn></mstyle></math> by <math><mstyle displaystyle="true"><mo>-</mo><mn>1</mn></mstyle></math> .

Multiply <math><mstyle displaystyle="true"><mo>-</mo><mn>1</mn></mstyle></math> by <math><mstyle displaystyle="true"><mn>18</mn></mstyle></math> .

Subtract <math><mstyle displaystyle="true"><mn>18</mn></mstyle></math> from <math><mstyle displaystyle="true"><mn>18</mn></mstyle></math> .

Add <math><mstyle displaystyle="true"><mo>-</mo><mn>13</mn><mi>x</mi></mstyle></math> and <math><mstyle displaystyle="true"><mn>0</mn></mstyle></math> .

Move the negative in front of the fraction.

Simplify the numerator.

Multiply <math><mstyle displaystyle="true"><mn>2</mn></mstyle></math> by <math><mstyle displaystyle="true"><mo>-</mo><mn>1</mn></mstyle></math> .

Combine <math><mstyle displaystyle="true"><mo>-</mo><mn>2</mn></mstyle></math> and <math><mstyle displaystyle="true"><mfrac><mrow><mn>13</mn><mi>x</mi></mrow><mrow><mn>2</mn></mrow></mfrac></mstyle></math> .

Multiply <math><mstyle displaystyle="true"><mo>-</mo><mn>2</mn></mstyle></math> by <math><mstyle displaystyle="true"><mn>13</mn></mstyle></math> .

Reduce the expression by cancelling the common factors.

Reduce the expression <math><mstyle displaystyle="true"><mfrac><mrow><mo>-</mo><mn>26</mn><mi>x</mi></mrow><mrow><mn>2</mn></mrow></mfrac></mstyle></math> by cancelling the common factors.

Factor <math><mstyle displaystyle="true"><mn>2</mn></mstyle></math> out of <math><mstyle displaystyle="true"><mo>-</mo><mn>26</mn><mi>x</mi></mstyle></math> .

Factor <math><mstyle displaystyle="true"><mn>2</mn></mstyle></math> out of <math><mstyle displaystyle="true"><mn>2</mn></mstyle></math> .

Cancel the common factor.

Rewrite the expression.

Divide <math><mstyle displaystyle="true"><mo>-</mo><mn>13</mn><mi>x</mi></mstyle></math> by <math><mstyle displaystyle="true"><mn>1</mn></mstyle></math> .

Cancel the common factor of <math><mstyle displaystyle="true"><mo>-</mo><mn>13</mn></mstyle></math> and <math><mstyle displaystyle="true"><mn>13</mn></mstyle></math> .

Factor <math><mstyle displaystyle="true"><mn>13</mn></mstyle></math> out of <math><mstyle displaystyle="true"><mo>-</mo><mn>13</mn><mi>x</mi></mstyle></math> .

Cancel the common factors.

Factor <math><mstyle displaystyle="true"><mn>13</mn></mstyle></math> out of <math><mstyle displaystyle="true"><mn>13</mn></mstyle></math> .

Cancel the common factor.

Rewrite the expression.

Divide <math><mstyle displaystyle="true"><mo>-</mo><mi>x</mi></mstyle></math> by <math><mstyle displaystyle="true"><mn>1</mn></mstyle></math> .

Since <math><mstyle displaystyle="true"><mi>g</mi><mrow><mo>(</mo><mi>f</mi><mrow><mo>(</mo><mi>x</mi><mo>)</mo></mrow><mo>)</mo></mrow><mo>=</mo><mi>x</mi></mstyle></math> , <math><mstyle displaystyle="true"><msup><mrow><mi>f</mi></mrow><mrow><mo>-</mo><mn>1</mn></mrow></msup><mrow><mo>(</mo><mi>x</mi><mo>)</mo></mrow><mo>=</mo><mo>-</mo><mfrac><mrow><mn>2</mn><mrow><mo>(</mo><mn>9</mn><mo>-</mo><msqrt><mn>81</mn><mo>+</mo><mn>26</mn><mi>x</mi></msqrt><mo>)</mo></mrow></mrow><mrow><mn>13</mn></mrow></mfrac><mo>,</mo><mo>-</mo><mfrac><mrow><mn>2</mn><mrow><mo>(</mo><mn>9</mn><mo>+</mo><msqrt><mn>26</mn><mi>x</mi><mo>+</mo><mn>81</mn></msqrt><mo>)</mo></mrow></mrow><mrow><mn>13</mn></mrow></mfrac></mstyle></math> is the inverse of <math><mstyle displaystyle="true"><mi>f</mi><mrow><mo>(</mo><mi>x</mi><mo>)</mo></mrow><mo>=</mo><mfrac><mrow><msup><mrow><mi>x</mi></mrow><mrow><mn>2</mn></mrow></msup></mrow><mrow><mn>8</mn></mrow></mfrac><mo>+</mo><mfrac><mrow><mn>3</mn><msup><mrow><mi>x</mi></mrow><mrow><mn>2</mn></mrow></msup></mrow><mrow><mn>2</mn></mrow></mfrac><mo>+</mo><mfrac><mrow><mn>9</mn><mi>x</mi></mrow><mrow><mn>2</mn></mrow></mfrac></mstyle></math> .

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