# Calculus Examples

Step 1

Write as an equation.

Step 2

Interchange the variables.

Step 3

Step 3.1

Rewrite the equation as .

Step 3.2

Take the specified root of both sides of the equation to eliminate the exponent on the left side.

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

Remove parentheses.

Step 5.2.4

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

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

Rewrite as .

Step 5.3.3.1

Use to rewrite as .

Step 5.3.3.2

Apply the power rule and multiply exponents, .

Step 5.3.3.3

Combine and .

Step 5.3.3.4

Cancel the common factor of .

Step 5.3.3.4.1

Cancel the common factor.

Step 5.3.3.4.2

Rewrite the expression.

Step 5.3.3.5

Simplify.

Step 5.4

Since and , then is the inverse of .