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Calculus 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
Simplify the numerator.
Step 4.2.3.1
Combine and .
Step 4.2.3.2
To write as a fraction with a common denominator, multiply by .
Step 4.2.3.3
Combine the numerators over the common denominator.
Step 4.2.3.4
Rewrite in a factored form.
Step 4.2.3.4.1
Apply the distributive property.
Step 4.2.3.4.2
Multiply by .
Step 4.2.3.4.3
Multiply by .
Step 4.2.3.4.4
Apply the distributive property.
Step 4.2.3.4.5
Multiply by .
Step 4.2.3.4.6
Multiply by .
Step 4.2.3.4.7
Add and .
Step 4.2.3.4.8
Add and .
Step 4.2.3.4.9
Add and .
Step 4.2.4
Simplify the denominator.
Step 4.2.4.1
Combine and .
Step 4.2.4.2
To write as a fraction with a common denominator, multiply by .
Step 4.2.4.3
Combine and .
Step 4.2.4.4
Combine the numerators over the common denominator.
Step 4.2.4.5
Rewrite in a factored form.
Step 4.2.4.5.1
Apply the distributive property.
Step 4.2.4.5.2
Multiply by .
Step 4.2.4.5.3
Multiply by .
Step 4.2.4.5.4
Apply the distributive property.
Step 4.2.4.5.5
Multiply by .
Step 4.2.4.5.6
Multiply by .
Step 4.2.4.5.7
Subtract from .
Step 4.2.4.5.8
Add and .
Step 4.2.4.5.9
Add and .
Step 4.2.5
Multiply the numerator by the reciprocal of the denominator.
Step 4.2.6
Cancel the common factor of .
Step 4.2.6.1
Factor out of .
Step 4.2.6.2
Cancel the common factor.
Step 4.2.6.3
Rewrite the expression.
Step 4.2.7
Cancel the common factor of .
Step 4.2.7.1
Cancel the common factor.
Step 4.2.7.2
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
Simplify the numerator.
Step 4.3.3.1
Combine and .
Step 4.3.3.2
To write as a fraction with a common denominator, multiply by .
Step 4.3.3.3
Combine the numerators over the common denominator.
Step 4.3.3.4
Reorder terms.
Step 4.3.3.5
Rewrite in a factored form.
Step 4.3.3.5.1
Apply the distributive property.
Step 4.3.3.5.2
Multiply by .
Step 4.3.3.5.3
Multiply by .
Step 4.3.3.5.4
Apply the distributive property.
Step 4.3.3.5.5
Multiply by .
Step 4.3.3.5.6
Multiply by .
Step 4.3.3.5.7
Add and .
Step 4.3.3.5.8
Add and .
Step 4.3.3.5.9
Add and .
Step 4.3.4
Simplify the denominator.
Step 4.3.4.1
Combine and .
Step 4.3.4.2
To write as a fraction with a common denominator, multiply by .
Step 4.3.4.3
Combine and .
Step 4.3.4.4
Combine the numerators over the common denominator.
Step 4.3.4.5
Rewrite in a factored form.
Step 4.3.4.5.1
Apply the distributive property.
Step 4.3.4.5.2
Multiply by .
Step 4.3.4.5.3
Multiply by .
Step 4.3.4.5.4
Apply the distributive property.
Step 4.3.4.5.5
Multiply by .
Step 4.3.4.5.6
Multiply by .
Step 4.3.4.5.7
Add and .
Step 4.3.4.5.8
Subtract from .
Step 4.3.4.5.9
Add and .
Step 4.3.5
Multiply the numerator by the reciprocal of the denominator.
Step 4.3.6
Cancel the common factor of .
Step 4.3.6.1
Factor out of .
Step 4.3.6.2
Cancel the common factor.
Step 4.3.6.3
Rewrite the expression.
Step 4.3.7
Cancel the common factor of .
Step 4.3.7.1
Cancel the common factor.
Step 4.3.7.2
Rewrite the expression.
Step 4.4
Since and , then is the inverse of .