Let f : R→R be given by f(x)

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).

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