If f : R → R is defined by
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, $f^{-1}(-25)=\phi$