# Precalculus Examples

Step 1
Write as an equation.
Step 2
Interchange the variables.
Step 3
Solve for .
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
Verify if is the inverse of .
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 .