# Precalculus Examples

Step 1
Write as an equation.
Step 2
Interchange the variables.
Step 3
Solve for .
Rewrite the equation as .
Add to both sides of the equation.
Divide each term in by and simplify.
Divide each term in by .
Simplify the left side.
Cancel the common factor of .
Cancel the common factor.
Divide by .
Simplify the right side.
Simplify each term.
Move the negative in front of the fraction.
Move the negative in front of the fraction.
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 .
Combine the numerators over the common denominator.
Simplify each term.
Apply the distributive property.
Multiply by .
Multiply by .
Simplify terms.
Combine the opposite terms in .
Subtract from .
Add and .
Cancel the common factor of .
Cancel the common factor.
Divide by .
Evaluate .
Set up the composite result function.
Evaluate by substituting in the value of into .
Simplify each term.
Apply the distributive property.
Cancel the common factor of .
Move the leading negative in into the numerator.
Factor out of .
Cancel the common factor.
Rewrite the expression.
Multiply by .
Multiply by .
Cancel the common factor of .
Move the leading negative in into the numerator.
Factor out of .
Cancel the common factor.
Rewrite the expression.
Multiply by .
Combine the opposite terms in .
Subtract from .
Add and .
Since and , then is the inverse of .
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