Practicing Success
Practicing Success
CUET Preparation Today
The function $f(x)=\tan ^{-1}(\tan x)$, is |
everywhere continuous discontinuous at $x=\frac{n \pi}{2}, n \in Z$ not differentiable at $x=(2 n+1) \frac{\pi}{2}, n \in Z$ such that f'(x) = 1 for all $x \in R-\left\{(2 n+1) \frac{\pi}{2}, n \in Z\right\}$ everywhere continuous and differentiable such that f'(x) = 1 for all $x \in R$ |
not differentiable at $x=(2 n+1) \frac{\pi}{2}, n \in Z$ such that f'(x) = 1 for all $x \in R-\left\{(2 n+1) \frac{\pi}{2}, n \in Z\right\}$ |
The graph of the function $f(x)=\tan ^{-1}(\tan x)$ is as given in Figure.
It is evident from the curve y = f(x) that f(x) is discontinuous and hence non-differentiable at $x=(2 n+1) \frac{\pi}{2}, n \in Z$ such that f'(x) = 1 for all $x \in R-\left\{(2 n+1) \frac{\pi}{2}, n \in Z\right\}$. |
