Question

Find the inverse of the function $y$ = $x^3$ - 1, x $ϵ(-\infty ,0].$

Answer 1

$f\left(x\right)=y=x^3-1$

$⟹x^3=y+1$

$⟹x=(y+1{)}^{\frac{1}{3}}$

$⟹f^{-1}\left(y\right)=(y+1{)}^{\frac{1}{3}}$

Replacing $y$ with $x$-

$⟹f^{-1}\left(x\right)=(x+1{)}^{\frac{1}{3}}$