Question:
If $f: R \rightarrow R$ is given by $f(x)=x^{3}$, write $f^{-1}$ (1)
Solution:
Let $f^{-1}(1)=x \quad \ldots(1)$
$\Rightarrow f(x)=1$
$\Rightarrow x^{3}=1$
$\Rightarrow x^{3}-1=0$
$\Rightarrow(x-1)\left(x^{2}+x+1\right)=0 \quad\left[\mathrm{u}\right.$ sing the identity $\left.: a^{3}-b^{3}=(a-b)\left(a^{2}+a b+b^{2}\right)\right]$
$\Rightarrow x=1 \quad($ as $x \in R)$
$\Rightarrow f^{-1}(1)=\{1\} \quad[$ from $(1)]$