Question

The set of extreme values of the function $f\left(x\right)=\tan x,x\in R-\left\{(2k+1)\left(\frac{\mathrm{\pi }}{2}\right),k\in I\right\}$

• A. $ɸ$
• B. $R–(-1,1)$
• C. $R^{+}\cup \left\{0\right\}$
• D. $R$

Answer 1

The correct option is A

$ɸ$

Explanation for the correct option.

Given, $f\left(x\right)=tanx,x\in R-\left\{(2k+1)\left(\frac{\mathrm{\pi }}{2}\right),k\in I\right\}$

$$\begin{gathered} f\left(x\right)=\tan x \\ f\text{'}\left(x\right)=se{c}^{2}x \\ f\text{'}\left(x\right)=0 \end{gathered}$$

$\Rightarrow se{c}^{2}x=0$

It is not possible, as $secx$ cannot take values between $\left(-1,1\right)$

Hence $secx\ne 0$

The set of extreme values of the function $=ɸ$

Hence, option (A) is the correct option.