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# Precalculus Examples

Step 1

Interchange the variables.

Step 2

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.

Subtract from both sides of the equation.

Step 3

Replace with to show the final answer.

Step 4

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.

Combine the opposite terms in .

Subtract from .

Add and .

Evaluate .

Set up the composite result function.

Evaluate by substituting in the value of into .

Add and .

Add and .

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

Since and , then is the inverse of .