I'm trying to find the domain and the form of the composition of the following functions: $f:y=\sqrt[3]{x}$ , $g:y=1-x^2$.

My solution is the following: domain = $[-1,1]$ , form = $f\circ g: y= 1-x^3$

My steps:

domain: $D(f\circ g)=${$x\in\mathbb{R}, 1-x^2\in\mathbb{R}^+$}, $\Rightarrow 1-x^2\geq 0$ $\Leftrightarrow x^2\leq 1$ $\Rightarrow x\in[-1,1]$

form: $1-(\sqrt{x^3})^2 \Leftrightarrow 1-x^3$

Is it correct? Thanks!