Question:
If $f: R \rightarrow R$ is given by $f(x)=x^{3}+3$, then $f^{-1}(x)$ is equal to
(a) $x^{1 / 3}-3$
(b) $x^{1 / 3}+3$
(c) $(x-3)^{1 / 3}$
(d) $x+3^{1 / 3}$
Solution:
(c)
Let $f^{-1}(x)=y$
$f(y)=x$
$\Rightarrow y^{3}+3=x$
$\Rightarrow y^{3}=x-3$
$\Rightarrow y=\sqrt[3]{x-3}$
$\Rightarrow y=(x-3)^{\frac{1}{3}}$
So, the answer is (c).
Click here to get exam-ready with eSaral
For making your preparation journey smoother of JEE, NEET and Class 8 to 10, grab our app now.