# Precalculus Examples

Step 1

Write as an equation.

Step 2

Interchange the variables.

Step 3

Step 3.1

Rewrite the equation as .

Step 3.2

Add to both sides of the equation.

Step 3.3

Divide each term in by and simplify.

Step 3.3.1

Divide each term in by .

Step 3.3.2

Simplify the left side.

Step 3.3.2.1

Cancel the common factor of .

Step 3.3.2.1.1

Cancel the common factor.

Step 3.3.2.1.2

Divide by .

Step 3.3.3

Simplify the right side.

Step 3.3.3.1

Simplify each term.

Step 3.3.3.1.1

Move the negative in front of the fraction.

Step 3.3.3.1.2

Move the negative in front of the fraction.

Step 4

Replace with to show the final answer.

Step 5

Step 5.1

To verify the inverse, check if and .

Step 5.2

Evaluate .

Step 5.2.1

Set up the composite result function.

Step 5.2.2

Evaluate by substituting in the value of into .

Step 5.2.3

Combine the numerators over the common denominator.

Step 5.2.4

Simplify each term.

Step 5.2.4.1

Apply the distributive property.

Step 5.2.4.2

Multiply by .

Step 5.2.4.3

Multiply by .

Step 5.2.5

Simplify terms.

Step 5.2.5.1

Combine the opposite terms in .

Step 5.2.5.1.1

Subtract from .

Step 5.2.5.1.2

Add and .

Step 5.2.5.2

Cancel the common factor of .

Step 5.2.5.2.1

Cancel the common factor.

Step 5.2.5.2.2

Divide by .

Step 5.3

Evaluate .

Step 5.3.1

Set up the composite result function.

Step 5.3.2

Evaluate by substituting in the value of into .

Step 5.3.3

Simplify each term.

Step 5.3.3.1

Apply the distributive property.

Step 5.3.3.2

Cancel the common factor of .

Step 5.3.3.2.1

Move the leading negative in into the numerator.

Step 5.3.3.2.2

Factor out of .

Step 5.3.3.2.3

Cancel the common factor.

Step 5.3.3.2.4

Rewrite the expression.

Step 5.3.3.3

Multiply by .

Step 5.3.3.4

Multiply by .

Step 5.3.3.5

Cancel the common factor of .

Step 5.3.3.5.1

Move the leading negative in into the numerator.

Step 5.3.3.5.2

Factor out of .

Step 5.3.3.5.3

Cancel the common factor.

Step 5.3.3.5.4

Rewrite the expression.

Step 5.3.3.6

Multiply by .

Step 5.3.4

Combine the opposite terms in .

Step 5.3.4.1

Subtract from .

Step 5.3.4.2

Add and .

Step 5.4

Since and , then is the inverse of .