Replace with .

Interchange the variables.

Rewrite the equation as .

Take the square root of each side of the equation to set up the solution for

Remove the perfect root factor under the radical to solve for .

The complete solution is the result of both the positive and negative portions of the solution.

First, use the positive value of the to find the first solution.

Subtract from both sides of the equation.

Divide each term by and simplify.

Divide each term in by .

Cancel the common factor of .

Cancel the common factor.

Divide by .

Simplify each term.

Move the negative in front of the fraction.

Dividing two negative values results in a positive value.

Next, use the negative value of the to find the second solution.

Subtract from both sides of the equation.

Divide each term by and simplify.

Divide each term in by .

Cancel the common factor of .

Cancel the common factor.

Divide by .

Simplify each term.

Dividing two negative values results in a positive value.

Dividing two negative values results in a positive value.

The complete solution is the result of both the positive and negative portions of the solution.

Replace the with to show the final answer.

Set up the composite result function.

Evaluate by substituting in the value of into .

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

Combine the numerators over the common denominator.

Simplify the numerator.

Apply the distributive property.

Multiply by .

Multiply by .

Add and .

Add and .

Cancel the common factor of .

Cancel the common factor.

Divide by .

Since , is the inverse of .

Find the Inverse f(x)=(7-8x)^2