Precalculus Examples

Find the Inverse f(x)=x/(x+4)
Step 1
Write as an equation.
Step 2
Interchange the variables.
Step 3
Solve for .
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Step 3.1
Rewrite the equation as .
Step 3.2
Find the LCD of the terms in the equation.
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Step 3.2.1
Finding the LCD of a list of values is the same as finding the LCM of the denominators of those values.
Step 3.2.2
Remove parentheses.
Step 3.2.3
The LCM of one and any expression is the expression.
Step 3.3
Multiply each term in by to eliminate the fractions.
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Step 3.3.1
Multiply each term in by .
Step 3.3.2
Simplify the left side.
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Step 3.3.2.1
Cancel the common factor of .
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Step 3.3.2.1.1
Cancel the common factor.
Step 3.3.2.1.2
Rewrite the expression.
Step 3.3.3
Simplify the right side.
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Step 3.3.3.1
Apply the distributive property.
Step 3.3.3.2
Move to the left of .
Step 3.4
Solve the equation.
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Step 3.4.1
Subtract from both sides of the equation.
Step 3.4.2
Factor out of .
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Step 3.4.2.1
Factor out of .
Step 3.4.2.2
Factor out of .
Step 3.4.2.3
Factor out of .
Step 3.4.3
Divide each term in by and simplify.
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Step 3.4.3.1
Divide each term in by .
Step 3.4.3.2
Simplify the left side.
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Step 3.4.3.2.1
Cancel the common factor of .
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Step 3.4.3.2.1.1
Cancel the common factor.
Step 3.4.3.2.1.2
Divide by .
Step 4
Replace with to show the final answer.
Step 5
Verify if is the inverse of .
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Step 5.1
To verify the inverse, check if and .
Step 5.2
Evaluate .
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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
Combine and .
Step 5.2.4
Simplify the denominator.
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Step 5.2.4.1
Write as a fraction with a common denominator.
Step 5.2.4.2
Combine the numerators over the common denominator.
Step 5.2.4.3
Reorder terms.
Step 5.2.4.4
Rewrite in a factored form.
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Step 5.2.4.4.1
Subtract from .
Step 5.2.4.4.2
Add and .
Step 5.2.5
Multiply the numerator by the reciprocal of the denominator.
Step 5.2.6
Cancel the common factor of .
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Step 5.2.6.1
Factor out of .
Step 5.2.6.2
Cancel the common factor.
Step 5.2.6.3
Rewrite the expression.
Step 5.2.7
Cancel the common factor of .
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Step 5.2.7.1
Cancel the common factor.
Step 5.2.7.2
Rewrite the expression.
Step 5.3
Evaluate .
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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
Multiply the numerator by the reciprocal of the denominator.
Step 5.3.4
Simplify the denominator.
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Step 5.3.4.1
To write as a fraction with a common denominator, multiply by .
Step 5.3.4.2
Combine the numerators over the common denominator.
Step 5.3.4.3
Reorder terms.
Step 5.3.4.4
Rewrite in a factored form.
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Step 5.3.4.4.1
Factor out of .
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Step 5.3.4.4.1.1
Factor out of .
Step 5.3.4.4.1.2
Factor out of .
Step 5.3.4.4.2
Subtract from .
Step 5.3.4.4.3
Add and .
Step 5.3.4.5
Multiply by .
Step 5.3.5
Multiply the numerator by the reciprocal of the denominator.
Step 5.3.6
Multiply by .
Step 5.3.7
Cancel the common factor of .
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Step 5.3.7.1
Factor out of .
Step 5.3.7.2
Cancel the common factor.
Step 5.3.7.3
Rewrite the expression.
Step 5.3.8
Multiply by .
Step 5.3.9
Cancel the common factor of and .
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Step 5.3.9.1
Reorder terms.
Step 5.3.9.2
Cancel the common factor.
Step 5.3.9.3
Divide by .
Step 5.4
Since and , then is the inverse of .