$f(x)=|x|⋅x$ what is the inverse at $f^{−1}(x)$ if $x≥0$ and the inverse at $f^{−1}(x)$ if $x≤0.$

Question

I tried this question and my only solution is that this is not possible or is there another way to solve this?

$f(x) = x|x| $

(Q): What is the inverse at $f^{−1}(x)$ if $x ≥ 0$ and the inverse at $f^{−1}(x)$ if $x≤0$.

Answer 1

We have

$f(x)=x^2$ if $x \ge 0$

and

$f(x)=-x^2$ if $x<0.$

Can you proceed ?