Question

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

• A. $\frac{\pi}{4}$
• B. $n\pi + \frac{\pi}{4}; \, n \in \mathbb{Z}$
• C. $\frac{\pi}{3}$
• D. $n\pi + \frac{\pi}{3}; \, n \in \mathbb{Z}$

Answer 1

The Correct Option is A

The function $\tan x$ is periodic with period $\pi$.

The principal value of $\tan^{-1}(1)$ is $x = \frac{\pi}{4}$. 

Hence, $f^{-1}(1) = \frac{\pi}{4}$.