Question

The function $f\left(x\right)=x-\tan x,$ in its domain

• A. Always increases
• B. Always decreases
• C. Is monotonic
• D. Is non-monotonic

Answer 1

Answer: (B), (C)

Is monotonic

Given, $f\left(x\right)=x-\tan x$
$\Rightarrow f^{\prime }\left(x\right)=1-{\sec }^{2}x$
$=-{\tan }^{2}x\le 0$ for all $x\in$ Domain of $f\left(x\right)$
$\therefore f\left(x\right)$ always decreases
$\Rightarrow f\left(x\right)$ is monotonic