Question: If $f: R \rightarrow R$ is defined by $f(x)=x^{2}$, find $f^{-1}(-25)$
Solution:
Let $f^{-1}(-25)=x$
$\Rightarrow f(x)=-25$
$\Rightarrow x^{2}=-25$
We cannot find $x \in R$, such that $x^{2}=-25$ (as $x^{2} \geq 0$ for all $x \in R$ )
So, $f^{-1}(-25)=\phi$
