If f : R→R is given by

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).

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