ANSWER
[tex]f^{-1}(x)=\sqrt[3]{\frac{7-x}{9}}[/tex]
EXPLANATION
We want to find the inverse function of the given function:
[tex]f(x)=7-9x^3[/tex]
To do this, we have to make x the subject of the formula.
Let f(x) be y:
[tex]\begin{gathered} y=7-9x^3 \\ 9x^3=7-y \\ x^3=\frac{7-y}{9} \\ \Rightarrow x=\sqrt[3]{\frac{7-y}{9}} \end{gathered}[/tex]
Now, replace x with f^(-1)(x) and y with x:
[tex]f^{-1}(x)=\sqrt[3]{\frac{7-x}{9}}[/tex]
That is the inverse function of f.
