To find the inverse function of [tex]\( f(x) = x^3 \)[/tex], we follow these steps:
1. Replace [tex]\( f(x) \)[/tex] with [tex]\( y \)[/tex]:
[tex]\[
y = x^3
\][/tex]
2. Swap [tex]\( x \)[/tex] and [tex]\( y \)[/tex] to find the inverse:
[tex]\[
x = y^3
\][/tex]
3. Solve for [tex]\( y \)[/tex]:
[tex]\[
y = x^{1/3}
\][/tex]
4. Since we denote the inverse function as [tex]\( f^{-1}(x) \)[/tex], we have:
[tex]\[
f^{-1}(x) = -1
\][/tex]
So, the inverse function [tex]\( f^{-1}(x) \)[/tex] is [tex]\(\boxed{-1}\)[/tex].
