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# Algebra Examples

Step 1

Interchange the variables.

Step 2

Step 2.1

Rewrite the equation as .

Step 2.2

Combine and .

Step 2.3

Add to both sides of the equation.

Step 2.4

Multiply both sides of the equation by .

Step 2.5

Simplify both sides of the equation.

Step 2.5.1

Simplify the left side.

Step 2.5.1.1

Cancel the common factor of .

Step 2.5.1.1.1

Cancel the common factor.

Step 2.5.1.1.2

Rewrite the expression.

Step 2.5.2

Simplify the right side.

Step 2.5.2.1

Simplify .

Step 2.5.2.1.1

Apply the distributive property.

Step 2.5.2.1.2

Multiply by .

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

Simplify each term.

Step 4.2.3.1

Combine and .

Step 4.2.3.2

Apply the distributive property.

Step 4.2.3.3

Cancel the common factor of .

Step 4.2.3.3.1

Cancel the common factor.

Step 4.2.3.3.2

Rewrite the expression.

Step 4.2.3.4

Multiply by .

Step 4.2.4

Combine the opposite terms in .

Step 4.2.4.1

Add and .

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

Simplify each term.

Step 4.3.3.1

Apply the distributive property.

Step 4.3.3.2

Cancel the common factor of .

Step 4.3.3.2.1

Factor out of .

Step 4.3.3.2.2

Cancel the common factor.

Step 4.3.3.2.3

Rewrite the expression.

Step 4.3.3.3

Cancel the common factor of .

Step 4.3.3.3.1

Factor out of .

Step 4.3.3.3.2

Cancel the common factor.

Step 4.3.3.3.3

Rewrite the expression.

Step 4.3.4

Combine the opposite terms in .

Step 4.3.4.1

Subtract from .

Step 4.3.4.2

Add and .

Step 4.4

Since and , then is the inverse of .