If $f:A\to A$ is defined by $f\left(x\right)=x^3$ where $A=\{x/-1\le x\le 1\}$, then f is

$f:A\to A,f\left(x\right)=x^3$

$A=\{x/-1\le x\le 1\}$

$f\left(x_1\right)=f\left(x_2\right)$

$x_1^3=x_2^3\iff x_1=x_2$ $\therefore$one-one

$f\left(x\right)=y$$\Rightarrow x^3=y\Rightarrow x=\sqrt[3]{y}\left(\text{or}\right)x\in [-1,1]\Rightarrow x^3\in [-1,1]\Rightarrow f\left(x\right)\in [-1,1]$

$\therefore$onto

$\therefore$Bijectio