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# Precalculus Examples

Step 1

Interchange the variables.

Step 2

Step 2.1

Rewrite the equation as .

Step 2.2

To remove the radical on the left side of the equation, square both sides of the equation.

Step 2.3

Simplify each side of the equation.

Step 2.3.1

Use to rewrite as .

Step 2.3.2

Simplify the left side.

Step 2.3.2.1

Simplify .

Step 2.3.2.1.1

Multiply the exponents in .

Step 2.3.2.1.1.1

Apply the power rule and multiply exponents, .

Step 2.3.2.1.1.2

Cancel the common factor of .

Step 2.3.2.1.1.2.1

Cancel the common factor.

Step 2.3.2.1.1.2.2

Rewrite the expression.

Step 2.3.2.1.2

Simplify.

Step 2.4

Subtract from both sides of the equation.

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

Rewrite as .

Step 4.2.3.1

Use to rewrite as .

Step 4.2.3.2

Apply the power rule and multiply exponents, .

Step 4.2.3.3

Combine and .

Step 4.2.3.4

Cancel the common factor of .

Step 4.2.3.4.1

Cancel the common factor.

Step 4.2.3.4.2

Rewrite the expression.

Step 4.2.3.5

Simplify.

Step 4.2.4

Combine the opposite terms in .

Step 4.2.4.1

Subtract from .

Step 4.2.4.2

Add and .

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

Add and .

Step 4.3.4

Add and .

Step 4.3.5

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

Step 4.4

Since and , then is the inverse of .