Q58 / 150 · MHT CET 2007 · Mathematics

If $f: R \rightarrow R$ be mapping defined by $f(x)=x^{3}+5$, then $f^{-1}(x)$ is equal to

  • A
    $(x+5)^{1 / 3}$
  • Correct answer
    B
    $(x-5)^{1 / 3}$
  • C
    $(5-x)^{1 / 3}$
  • D
    $5-x$

Solution

Let $$ y=f(x)=x^{3}+5 $$ $$ \begin{array}{lr} \Rightarrow \quad x=(y-5)^{1 / 3} \\ \therefore \quad f^{-1}(x)=(x-5)^{1 / 3} \\ \text { Given, } & f(x)=\frac{a x+b}{c x+d} \end{array} $$

Hence, the correct answer is option: 'B'.

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