The range is the set of all valid <math><mstyle displaystyle="true"><mi>y</mi></mstyle></math> values. Use the graph to find the range.

Convert <math><mstyle displaystyle="true"><mrow><mo>[</mo><mo>-</mo><mn>7</mn><mo>,</mo><mi>∞</mi><mo>)</mo></mrow></mstyle></math> to an inequality.

Interchange the variables.

Solve for <math><mstyle displaystyle="true"><mi>y</mi></mstyle></math> .

Rewrite the equation as <math><mstyle displaystyle="true"><mn>2</mn><msup><mrow><mi>y</mi></mrow><mrow><mn>2</mn></mrow></msup><mo>-</mo><mn>8</mn><mi>y</mi><mo>+</mo><mn>1</mn><mo>=</mo><mi>x</mi></mstyle></math> .

Subtract <math><mstyle displaystyle="true"><mi>x</mi></mstyle></math> from both sides of the equation.

Use the quadratic formula to find the solutions.

Substitute the values <math><mstyle displaystyle="true"><mi>a</mi><mo>=</mo><mn>2</mn></mstyle></math> , <math><mstyle displaystyle="true"><mi>b</mi><mo>=</mo><mo>-</mo><mn>8</mn></mstyle></math> , and <math><mstyle displaystyle="true"><mi>c</mi><mo>=</mo><mn>1</mn><mo>-</mo><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"><mo>-</mo><mn>8</mn></mstyle></math> to the power of <math><mstyle displaystyle="true"><mn>2</mn></mstyle></math> .

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

Apply the distributive property.

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

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

Subtract <math><mstyle displaystyle="true"><mn>8</mn></mstyle></math> from <math><mstyle displaystyle="true"><mn>64</mn></mstyle></math> .

Factor <math><mstyle displaystyle="true"><mn>8</mn></mstyle></math> out of <math><mstyle displaystyle="true"><mn>56</mn><mo>+</mo><mn>8</mn><mi>x</mi></mstyle></math> .

Factor <math><mstyle displaystyle="true"><mn>8</mn></mstyle></math> out of <math><mstyle displaystyle="true"><mn>56</mn></mstyle></math> .

Factor <math><mstyle displaystyle="true"><mn>8</mn></mstyle></math> out of <math><mstyle displaystyle="true"><mn>8</mn><mo>⋅</mo><mn>7</mn><mo>+</mo><mn>8</mn><mi>x</mi></mstyle></math> .

Rewrite <math><mstyle displaystyle="true"><mn>8</mn><mrow><mo>(</mo><mn>7</mn><mo>+</mo><mi>x</mi><mo>)</mo></mrow></mstyle></math> as <math><mstyle displaystyle="true"><msup><mrow><mn>2</mn></mrow><mrow><mn>2</mn></mrow></msup><mo>⋅</mo><mrow><mo>(</mo><mn>2</mn><mrow><mo>(</mo><mn>7</mn><mo>+</mo><mi>x</mi><mo>)</mo></mrow><mo>)</mo></mrow></mstyle></math> .

Factor <math><mstyle displaystyle="true"><mn>4</mn></mstyle></math> out of <math><mstyle displaystyle="true"><mn>8</mn></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> .

Add parentheses.

Pull terms out from under the radical.

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

Simplify <math><mstyle displaystyle="true"><mfrac><mrow><mn>8</mn><mo>±</mo><mn>2</mn><msqrt><mn>2</mn><mrow><mo>(</mo><mn>7</mn><mo>+</mo><mi>x</mi><mo>)</mo></mrow></msqrt></mrow><mrow><mn>4</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"><mo>-</mo><mn>8</mn></mstyle></math> to the power of <math><mstyle displaystyle="true"><mn>2</mn></mstyle></math> .

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

Apply the distributive property.

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

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

Subtract <math><mstyle displaystyle="true"><mn>8</mn></mstyle></math> from <math><mstyle displaystyle="true"><mn>64</mn></mstyle></math> .

Factor <math><mstyle displaystyle="true"><mn>8</mn></mstyle></math> out of <math><mstyle displaystyle="true"><mn>56</mn><mo>+</mo><mn>8</mn><mi>x</mi></mstyle></math> .

Factor <math><mstyle displaystyle="true"><mn>8</mn></mstyle></math> out of <math><mstyle displaystyle="true"><mn>56</mn></mstyle></math> .

Factor <math><mstyle displaystyle="true"><mn>8</mn></mstyle></math> out of <math><mstyle displaystyle="true"><mn>8</mn><mo>⋅</mo><mn>7</mn><mo>+</mo><mn>8</mn><mi>x</mi></mstyle></math> .

Rewrite <math><mstyle displaystyle="true"><mn>8</mn><mrow><mo>(</mo><mn>7</mn><mo>+</mo><mi>x</mi><mo>)</mo></mrow></mstyle></math> as <math><mstyle displaystyle="true"><msup><mrow><mn>2</mn></mrow><mrow><mn>2</mn></mrow></msup><mo>⋅</mo><mrow><mo>(</mo><mn>2</mn><mrow><mo>(</mo><mn>7</mn><mo>+</mo><mi>x</mi><mo>)</mo></mrow><mo>)</mo></mrow></mstyle></math> .

Factor <math><mstyle displaystyle="true"><mn>4</mn></mstyle></math> out of <math><mstyle displaystyle="true"><mn>8</mn></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> .

Add parentheses.

Pull terms out from under the radical.

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

Simplify <math><mstyle displaystyle="true"><mfrac><mrow><mn>8</mn><mo>±</mo><mn>2</mn><msqrt><mn>2</mn><mrow><mo>(</mo><mn>7</mn><mo>+</mo><mi>x</mi><mo>)</mo></mrow></msqrt></mrow><mrow><mn>4</mn></mrow></mfrac></mstyle></math> .

Change the <math><mstyle displaystyle="true"><mo>±</mo></mstyle></math> to <math><mstyle displaystyle="true"><mo>+</mo></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"><mo>-</mo><mn>8</mn></mstyle></math> to the power of <math><mstyle displaystyle="true"><mn>2</mn></mstyle></math> .

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

Apply the distributive property.

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

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

Subtract <math><mstyle displaystyle="true"><mn>8</mn></mstyle></math> from <math><mstyle displaystyle="true"><mn>64</mn></mstyle></math> .

Factor <math><mstyle displaystyle="true"><mn>8</mn></mstyle></math> out of <math><mstyle displaystyle="true"><mn>56</mn><mo>+</mo><mn>8</mn><mi>x</mi></mstyle></math> .

Factor <math><mstyle displaystyle="true"><mn>8</mn></mstyle></math> out of <math><mstyle displaystyle="true"><mn>56</mn></mstyle></math> .

Factor <math><mstyle displaystyle="true"><mn>8</mn></mstyle></math> out of <math><mstyle displaystyle="true"><mn>8</mn><mo>⋅</mo><mn>7</mn><mo>+</mo><mn>8</mn><mi>x</mi></mstyle></math> .

Rewrite <math><mstyle displaystyle="true"><mn>8</mn><mrow><mo>(</mo><mn>7</mn><mo>+</mo><mi>x</mi><mo>)</mo></mrow></mstyle></math> as <math><mstyle displaystyle="true"><msup><mrow><mn>2</mn></mrow><mrow><mn>2</mn></mrow></msup><mo>⋅</mo><mrow><mo>(</mo><mn>2</mn><mrow><mo>(</mo><mn>7</mn><mo>+</mo><mi>x</mi><mo>)</mo></mrow><mo>)</mo></mrow></mstyle></math> .

Factor <math><mstyle displaystyle="true"><mn>4</mn></mstyle></math> out of <math><mstyle displaystyle="true"><mn>8</mn></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> .

Add parentheses.

Pull terms out from under the radical.

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

Simplify <math><mstyle displaystyle="true"><mfrac><mrow><mn>8</mn><mo>±</mo><mn>2</mn><msqrt><mn>2</mn><mrow><mo>(</mo><mn>7</mn><mo>+</mo><mi>x</mi><mo>)</mo></mrow></msqrt></mrow><mrow><mn>4</mn></mrow></mfrac></mstyle></math> .

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

The final answer is the combination of both solutions.

Replace <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.

Find the inverse using the domain and the range of the original function.

Do you know how to Find the Inverse f(x)=2x^2-8x+1 , x>=2? If not, you can write to our math experts in our application. The best solution for your task you can find above on this page.