# Calculus Examples

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