Question

Given f(x) = x3 - 5, find f-'(x).

Answer 1

the inverse function = f^-1(x) is option C

First let's state what we are given:

f(x) = x^3 - 5

We are to find the inverse of f(x).

To do this, first let's represent f(x) with y

y = = x^3 - 5

Then, we would interchange x and y

`\begin{gathered} x=y^3\text{ - 5 (make y the subject of formula)} \\ x+5=y^3 \\ find\text{ cube root both sides} \\ \sqrt[3]{y^3\text{ }}=\sqrt[3]{(x+5)} \\ y\text{ = }\sqrt[3]{(x+5)} \end{gathered}`

From the answer we got, the inverse function = f^-1(x) is option C