# Find the Inverse f(x)=(2x+1)^3-4 Replace with .
Interchange the variables.
Solve for .
Rewrite the equation as .
Add to both sides of the equation.
Take the cube root of each side of the equation to set up the solution for
Remove the perfect root factor under the radical to solve for .
Subtract from both sides of the equation.
Divide each term by and simplify.
Divide each term in by .
Cancel the common factor of .
Cancel the common factor.
Divide by .
Solve for and replace with .
Replace the with to show the final answer.
Set up the composite result function.
Evaluate by substituting in the value of into .
Simplify the numerator.
Use the Binomial Theorem.
Simplify each term.
Apply the product rule to .
Raise to the power of .
Apply the product rule to .
Raise to the power of .
Multiply by .
Multiply by .
Multiply by .
One to any power is one.
Multiply by .
One to any power is one.
Subtract from .
Rewrite in a factored form.
Regroup terms.
Rewrite as .
Rewrite as .
Since both terms are perfect cubes, factor using the sum of cubes formula, where and .
Simplify.
Apply the product rule to .
Raise to the power of .
Multiply by .
Multiply by .
One to any power is one.
Factor out of .
Factor out of .
Factor out of .
Factor out of .
Factor out of .
Factor out of .
Factor out of .
Factor using the perfect square rule.
Rewrite as .
Rewrite as .
Check the middle term by multiplying and compare this result with the middle term in the original expression.
Simplify.
Factor using the perfect square trinomial rule , where and .
Multiply by by adding the exponents.
Multiply by .
Raise to the power of .
Use the power rule to combine exponents.
Pull terms out from under the radical, assuming real numbers.
Subtract from .
Cancel the common factor of .
Cancel the common factor.
Divide by .
Since , is the inverse of .
Find the Inverse f(x)=(2x+1)^3-4     