Algebra Examples

Find the Inverse f(x)=(2x-5)/3
Step 1
Write as an equation.
Step 2
Interchange the variables.
Step 3
Solve for .
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Rewrite the equation as .
Multiply both sides by .
Simplify.
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Simplify the left side.
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Cancel the common factor of .
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Cancel the common factor.
Rewrite the expression.
Simplify the right side.
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Move to the left of .
Solve for .
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Add to both sides of the equation.
Divide each term in by and simplify.
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Divide each term in by .
Simplify the left side.
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Cancel the common factor of .
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Cancel the common factor.
Divide by .
Step 4
Replace with to show the final answer.
Step 5
Verify if is the inverse of .
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To verify the inverse, check if and .
Evaluate .
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Set up the composite result function.
Evaluate by substituting in the value of into .
Combine the numerators over the common denominator.
Cancel the common factor of .
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Cancel the common factor.
Rewrite the expression.
Combine the opposite terms in .
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Add and .
Add and .
Cancel the common factor of .
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Cancel the common factor.
Divide by .
Evaluate .
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Set up the composite result function.
Evaluate by substituting in the value of into .
Simplify the numerator.
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Apply the distributive property.
Cancel the common factor of .
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Cancel the common factor.
Rewrite the expression.
Cancel the common factor of .
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Cancel the common factor.
Rewrite the expression.
Subtract from .
Add and .
Cancel the common factor of .
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Cancel the common factor.
Divide by .
Since and , then is the inverse of .
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