# Find the Inverse (x^2)/8+(3x^2)/2+(9x)/2

Find the Inverse (x^2)/8+(3x^2)/2+(9x)/2
Interchange the variables.
Solve for .
Rewrite the equation as .
Simplify .
To write as a fraction with a common denominator, multiply by .
Write each expression with a common denominator of , by multiplying each by an appropriate factor of .
Multiply and .
Multiply by .
Combine the numerators over the common denominator.
Simplify each term.
Simplify the numerator.
Factor out of .
Multiply by .
Factor out of .
Factor out of .
Multiply by .
Move to the left of .
Move to the left side of the equation by subtracting it from both sides.
Multiply through by the least common denominator , then simplify.
Apply the distributive property.
Simplify.
Cancel the common factor of .
Cancel the common factor.
Rewrite the expression.
Cancel the common factor of .
Factor out of .
Cancel the common factor.
Rewrite the expression.
Multiply by .
Multiply by .
Move .
Use the quadratic formula to find the solutions.
Substitute the values , , and into the quadratic formula and solve for .
Simplify.
Simplify the numerator.
Raise to the power of .
Multiply by .
Multiply by .
Factor out of .
Factor out of .
Factor out of .
Factor out of .
Rewrite as .
Rewrite as .
Rewrite as .
Pull terms out from under the radical.
Raise to the power of .
Multiply by .
Simplify .
Simplify the expression to solve for the portion of the .
Simplify the numerator.
Raise to the power of .
Multiply by .
Multiply by .
Factor out of .
Factor out of .
Factor out of .
Factor out of .
Rewrite as .
Rewrite as .
Rewrite as .
Pull terms out from under the radical.
Raise to the power of .
Multiply by .
Simplify .
Change the to .
Factor out of .
Factor out of .
Factor out of .
Rewrite as .
Factor out of .
Factor out of .
Move the negative in front of the fraction.
Simplify the expression to solve for the portion of the .
Simplify the numerator.
Raise to the power of .
Multiply by .
Multiply by .
Factor out of .
Factor out of .
Factor out of .
Factor out of .
Rewrite as .
Rewrite as .
Rewrite as .
Pull terms out from under the radical.
Raise to the power of .
Multiply by .
Simplify .
Change the to .
Factor out of .
Reorder and .
Factor out of .
Factor out of .
Factor out of .
Move the negative in front of the fraction.
The final answer is the combination of both solutions.
Solve for and replace with .
Replace the with to show the final answer.
Set up the composite result function.
Evaluate by substituting in the value of into .
Simplify the numerator.
To write as a fraction with a common denominator, multiply by .
Write each expression with a common denominator of , by multiplying each by an appropriate factor of .
Multiply and .
Multiply by .
Combine the numerators over the common denominator.
Simplify each term.
Simplify the numerator.
Factor out of .
Multiply by .
Factor out of .
Factor out of .
Multiply by .
Move to the left of .
Apply the distributive property.
Cancel the common factor of .
Factor out of .
Factor out of .
Cancel the common factor.
Rewrite the expression.
Combine and .
Multiply by .
Cancel the common factor of .
Factor out of .
Cancel the common factor.
Rewrite the expression.
Multiply by .
Reorder terms.
Factor using the perfect square rule.
Rewrite as .
Rewrite as .
Rewrite as .
Rewrite as .
Check the middle term by multiplying and compare this result with the middle term in the original expression.
Simplify.
Factor using the perfect square trinomial rule , where and .
To write as a fraction with a common denominator, multiply by .
Combine and .
Combine the numerators over the common denominator.
Multiply by .
Apply the product rule to .
Raise to the power of .
Rewrite as .
Rewrite as .
Pull terms out from under the radical, assuming positive real numbers.
To write as a fraction with a common denominator, multiply by .
Combine and .
Combine the numerators over the common denominator.
Rewrite in a factored form.
Multiply by .
Apply the distributive property.
Multiply by .
Multiply by .
Subtract from .
Move the negative in front of the fraction.
Simplify the numerator.
Multiply by .
Combine and .
Multiply by .
Reduce the expression by cancelling the common factors.
Reduce the expression by cancelling the common factors.
Factor out of .
Factor out of .
Cancel the common factor.
Rewrite the expression.
Divide by .
Cancel the common factor of and .
Factor out of .
Cancel the common factors.
Factor out of .
Cancel the common factor.
Rewrite the expression.
Divide by .
Since , is the inverse of .
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