Question

pl

Answer 1

is your question like this?
\[f(x)=\frac{ x ^{\frac{ 1 }{ 3 }} }{ 9 }-4\]

Answer 2

let f(x)=y
\[y=\frac{ x ^{\frac{ 1 }{ 3 }} }{ 9 }-4\]
flip x and y and then solve for y

Answer 3

Let f(x)=y
\[y=\left( \frac{ x }{ 9 } \right)^{\frac{ 1 }{ 3 }}-4\]
flip x and y
\[x=\left( \frac{ y }{ 9 } \right)^{\frac{ 1 }{ 3 }}-4\]
\[\left( \frac{ y }{ 9 } \right)^{\frac{ 1 }{ 3 }}=x+4\]
cubing both sides
\[\frac{ y }{ 9 }=\left( x+4 \right)^3\]
\[f ^{-1}(x)=y=9(x+4)^3\]