Question

Find the inverse function of f.f(x) = 7 - 9x3f^-1(x) =

Answer 1

`f^(-1)(x)=\sqrt[3]{(7-x)/(9)}`

Step-by-step explanation

We want to find the inverse function of the given function:

`f(x)=7-9x^3`

To do this, we have to make x the subject of the formula.

Let f(x) be y:

`\begin{gathered} y=7-9x^3 \\ 9x^3=7-y \\ x^3=(7-y)/(9) \\ \Rightarrow x=\sqrt[3]{(7-y)/(9)} \end{gathered}`

Now, replace x with f^(-1)(x) and y with x:

`f^(-1)(x)=\sqrt[3]{(7-x)/(9)}`

That is the inverse function of f.