Question: Let $f: R \rightarrow R$ be given by $f(x)=x^{2}-3$. Then, $f^{-1}$ is given by
(a) $\sqrt{x+3}$
(b) $\sqrt{x}+3$
(c) $x+\sqrt{3}$
(d) None of these
Solution:
(d)
Let $f^{-1}(x)=y$
$f(y)=x$
$y^{2}-3=x$
$y^{2}=x+3$
$y=\pm \sqrt{x+3}$
So, the answer is (d).
