Question

Let $f:R\to R$ be given by $f\left(x\right)=x^2-3$. Then, $f^{-1}$ is given by
(a) $\sqrt{x+3}$
(b) $\sqrt{x}+3$
(c) $x+\sqrt{3}$
(d) None of these

Answer 1

(d)

$$\begin{gathered} \text{Let}{f}^{-1}\left(x\right)=y \\ f\left(y\right)=x \\ {y}^2-3=x \\ {y}^2=x+3 \\ y=\pm \sqrt{x+3} \end{gathered}$$
So, the answer is (d).