Q75 / 120 · VITEEE 2011 · Mathematics

Let $f: R \rightarrow R$ bedefined as $f(x)=x^{2}+1$, find $f^{-1}(-5)$.

  • A
    $\{\phi\}$
  • Correct answer
    B
    $\phi$
  • C
    $\{5\}$
  • D
    $\{-5,5\}$

Solution

Let $\mathrm{f}^{-1}(-5)=\mathrm{x}$. Then, $\mathrm{f}(\mathrm{x})=-5$ $$ \Rightarrow x^{2}+1=-5 \Rightarrow x^{2}=-6 \Rightarrow x=\pm \sqrt{-6} $$ which does not belong to $\mathrm{R}$. $$ \therefore \mathrm{f}^{-1}(-5)=\phi $$

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

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