Q76 / 180 · KCET 2024 · Mathematics

Let $f: R \rightarrow R$ be given $f(x)=\tan x$. Then, $f^{-1}(1)$ is

  • Correct answer
    A
    $\frac{\pi}{4}$
  • B
    $\left\{n \pi+\frac{\pi}{4}: n \in Z\right\}$
  • C
    $\frac{\pi}{3}$
  • D
    $\left\{n \pi+\frac{\pi}{3}: n \in Z\right\}$

Solution

$\because f(x)=\tan x$ Since, $f^{-1}$ is inverse of $f$ $\Rightarrow \quad f\left(f^{-1}(l)\right)=1$ $\Rightarrow \quad \tan \left(f^{-1}(1)\right)=1$ But $\quad \tan \left(\frac{\pi}{4}\right)=1$ $\Rightarrow \quad \tan \left(f^{-1}(1)\right)=\tan \left(\frac{\pi}{4}\right)$ $\therefore \quad f^{-1}(\mathrm{l})=\frac{\pi}{4}$

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

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