Q96 / 180 · KCET 2008 · Mathematics

If $\mathrm{f}: \mathrm{R} \rightarrow \mathrm{R}$ is defined by $\mathrm{f}(\mathrm{x})=\mathrm{x}^{3}$, then $\mathrm{f}^{-1}(8)$ is equal to

  • Correct answer
    A
    $\{2\}$
  • B
    $\left\{2,2 \omega, 2 \omega^{2}\right\}$
  • C
    $\{2,-2\}$
  • D
    $\{2,2\}$

Solution

Let $$ y=f(x)=x^{3} $$ $\therefore$ $\mathrm{x}=\mathrm{y}^{1 / 3}$ $\Rightarrow \quad \mathrm{f}^{-1}(\mathrm{x})=\mathrm{x}^{1 / 3}$ $\Rightarrow \quad \mathrm{f}^{-1}(8)=(8)^{1 / 3}$ $=2$

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

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