# Precalculus Examples

Step 1

Write as an equation.

Step 2

Interchange the variables.

Step 3

Rewrite the equation as .

To remove the radical on the left side of the equation, square both sides of the equation.

Simplify each side of the equation.

Use to rewrite as .

Simplify the left side.

Simplify .

Multiply the exponents in .

Apply the power rule and multiply exponents, .

Cancel the common factor of .

Cancel the common factor.

Rewrite the expression.

Simplify.

Step 4

Replace with to show the final answer.

Step 5

To verify the inverse, check if and .

Evaluate .

Set up the composite result function.

Evaluate by substituting in the value of into .

Rewrite as .

Use to rewrite as .

Apply the power rule and multiply exponents, .

Combine and .

Cancel the common factor of .

Cancel the common factor.

Rewrite the expression.

Simplify.

Evaluate .

Set up the composite result function.

Evaluate by substituting in the value of into .

Remove parentheses.

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

Since and , then is the inverse of .