Question
If $f:R \to R$ be given by $f(x) = \tan x$, then ${f^{ - 1}}(1)$ is
- (a) None of these ✓ Correct
- (b) $\frac{\pi }{4}$
- (c) $\left\{ {n\pi + \frac{\pi }{4}:n \in Z} \right\}$
- (d) Does not exist
Relations and Functions — Class 12 Maths Solution
Step-by-step Solution
It is given that,, $f(x) = \tan x$
Let $y = \tan x \Rightarrow x = {\tan ^{ - 1}}y$
$\Rightarrow$ ${f^{ - 1}}(x) = {\tan ^{ - 1}}x \Rightarrow {f^{ - 1}}(1) = {\tan ^{ - 1}}1$
$\Rightarrow$ $= {\tan ^{ - 1}}\tan \frac{\pi }{4} = \frac{\pi }{4}$
NCERT & Exemplar solution for CBSE Class 12 Mathematics, Relations and Functions. Curated by Sachin Sharma. Free for all students.