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Precalculus Examples
Step 1
Interchange the variables.
Step 2
Step 2.1
Multiply the equation by .
Step 2.2
Simplify the left side.
Step 2.2.1
Apply the distributive property.
Step 2.3
Simplify the right side.
Step 2.3.1
Cancel the common factor of .
Step 2.3.1.1
Cancel the common factor.
Step 2.3.1.2
Rewrite the expression.
Step 2.4
Solve for .
Step 2.4.1
Subtract from both sides of the equation.
Step 2.4.2
Add to both sides of the equation.
Step 2.4.3
Factor out of .
Step 2.4.3.1
Factor out of .
Step 2.4.3.2
Factor out of .
Step 2.4.3.3
Factor out of .
Step 2.4.4
Divide each term in by and simplify.
Step 2.4.4.1
Divide each term in by .
Step 2.4.4.2
Simplify the left side.
Step 2.4.4.2.1
Cancel the common factor of .
Step 2.4.4.2.1.1
Cancel the common factor.
Step 2.4.4.2.1.2
Divide by .
Step 2.4.4.3
Simplify the right side.
Step 2.4.4.3.1
Combine the numerators over the common denominator.
Step 3
Replace with to show the final answer.
Step 4
Step 4.1
To verify the inverse, check if and .
Step 4.2
Evaluate .
Step 4.2.1
Set up the composite result function.
Step 4.2.2
Evaluate by substituting in the value of into .
Step 4.2.3
Multiply the numerator and denominator of the fraction by .
Step 4.2.3.1
Multiply by .
Step 4.2.3.2
Combine.
Step 4.2.4
Apply the distributive property.
Step 4.2.5
Cancel the common factor of .
Step 4.2.5.1
Cancel the common factor.
Step 4.2.5.2
Rewrite the expression.
Step 4.2.6
Simplify the numerator.
Step 4.2.6.1
Factor out of .
Step 4.2.6.1.1
Factor out of .
Step 4.2.6.1.2
Factor out of .
Step 4.2.6.2
Combine and .
Step 4.2.6.3
To write as a fraction with a common denominator, multiply by .
Step 4.2.6.4
Combine the numerators over the common denominator.
Step 4.2.6.5
Reorder terms.
Step 4.2.6.6
Rewrite in a factored form.
Step 4.2.6.6.1
Apply the distributive property.
Step 4.2.6.6.2
Multiply by .
Step 4.2.6.6.3
Apply the distributive property.
Step 4.2.6.6.4
Multiply by .
Step 4.2.6.6.5
Add and .
Step 4.2.6.6.6
Subtract from .
Step 4.2.6.6.7
Add and .
Step 4.2.7
Simplify the denominator.
Step 4.2.7.1
Apply the distributive property.
Step 4.2.7.2
Move to the left of .
Step 4.2.7.3
Multiply by .
Step 4.2.7.4
Rewrite as .
Step 4.2.7.5
Subtract from .
Step 4.2.7.6
Add and .
Step 4.2.7.7
Add and .
Step 4.2.8
Reduce the expression by cancelling the common factors.
Step 4.2.8.1
Factor out of .
Step 4.2.8.2
Cancel the common factor of .
Step 4.2.8.2.1
Factor out of .
Step 4.2.8.2.2
Cancel the common factor.
Step 4.2.8.2.3
Rewrite the expression.
Step 4.2.8.3
Cancel the common factor of .
Step 4.2.8.3.1
Cancel the common factor.
Step 4.2.8.3.2
Rewrite the expression.
Step 4.3
Evaluate .
Step 4.3.1
Set up the composite result function.
Step 4.3.2
Evaluate by substituting in the value of into .
Step 4.3.3
Multiply the numerator and denominator of the fraction by .
Step 4.3.3.1
Multiply by .
Step 4.3.3.2
Combine.
Step 4.3.4
Apply the distributive property.
Step 4.3.5
Simplify by cancelling.
Step 4.3.5.1
Cancel the common factor of .
Step 4.3.5.1.1
Cancel the common factor.
Step 4.3.5.1.2
Rewrite the expression.
Step 4.3.5.2
Cancel the common factor of .
Step 4.3.5.2.1
Cancel the common factor.
Step 4.3.5.2.2
Rewrite the expression.
Step 4.3.6
Simplify the numerator.
Step 4.3.6.1
Apply the distributive property.
Step 4.3.6.2
Move to the left of .
Step 4.3.6.3
Multiply by .
Step 4.3.6.4
Subtract from .
Step 4.3.6.5
Add and .
Step 4.3.6.6
Add and .
Step 4.3.7
Simplify the denominator.
Step 4.3.7.1
Apply the distributive property.
Step 4.3.7.2
Move to the left of .
Step 4.3.7.3
Multiply by .
Step 4.3.7.4
Add and .
Step 4.3.7.5
Subtract from .
Step 4.3.7.6
Add and .
Step 4.3.8
Cancel the common factor of .
Step 4.3.8.1
Cancel the common factor.
Step 4.3.8.2
Divide by .
Step 4.4
Since and , then is the inverse of .