Question

What is the inverse of f(x)=(2x-1)^3

Answer 1

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Answer:

`f^(-1)(x)=\frac{\sqrt[3]{x}+1}{2}}`

Explanation:

Interchange x and y in the function definition and solve for y.

`x=(2y-1)^3\\\\\sqrt[3]{x}=2y-1\qquad\text{take cube root}\\\\\sqrt[3]{x}+1=2y\qquad\text{add 1}\\\\y=\frac{\sqrt[3]{x}+1}{2}\qquad\text{divide by 2}\\\\\boxed{f^(-1)(x)=\frac{\sqrt[3]{x}+1}{2}}`