Mark the correct alternative in the following question:

Question:

Mark the correct alternative in the following question:

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

(a) $\frac{\pi}{4}$

(b) $\left\{n \pi+\frac{\pi}{4}: n \in \mathbf{Z}\right\}$

(c) does not exist

 

(d) none of these

Solution:

We have,

$f: \mathbf{R} \rightarrow \mathbf{R}$ is given by

$f(x)=\tan x$

$\Rightarrow f^{-1}(x)=\tan ^{-1} x$

$\therefore f^{-1}(1)=\tan ^{-1} 1=\left\{n \pi+\frac{\pi}{4}: n \in \mathbf{Z}\right\}$

Hence, the correct alternative is option (b).

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