Question

The range of the function $f\left(x\right)=\frac{1-\tan x}{1+\tan x}$ is

• A. R-{0}
• B. R
• C. R-{-1}
• D. R-{1}

Answer 1

The correct option is B R

Given

$f\left(x\right)=\frac{1-\tan x}{1+\tan x}$

$\frac{\tan \frac{\pi }{4}-\tan x}{1+\tan \frac{\pi }{4}\tan x}$

$f\left(x\right)=\tan (\frac{\pi }{4}+x)$

$=\tan \theta$ where $\theta =\frac{\pi }{4}+x$

As we know range of $\tan \theta$ is $R$ i.e $(-\infty ,\infty )$

$\therefore$ Range of $f\left(x\right)$ is $R$