Question

Let $f:R\to R$ be given by

$f\left(x\right)=tanx.\text{Then}{f}^{-1}\left(1\right)$ is

• A. None of these
• B. $\frac{\pi }{4}$
• C. does not exist
• D. $\{n\pi +\frac{\pi }{4}:n\in Z\}$

Answer 1

The correct option is C does not exist

Given : $f:R\to R$ be given by $f\left(x\right)=tanx.$

We know,

$tan\frac{\pi }{4}=tan\frac{3\pi }{4}$

So, $f\left(x\right)$ is many one.

$\therefore f^{-1}\left(x\right)$ doesn't exist.