Question

The function $f\left(x\right)={\tan }^{-1}x-x$ is monotonically decreasing in the set

• A. $R$
• B. $(0,+\infty )$
• C. $R-\left\{0\right\}$
• D. none of these

Answer 1

Answer: (C)

$R-\left\{0\right\}$

$f\left(x\right)={\tan }^{-1}x-x$
For monotonically decreasing $f^{\prime }\left(x\right)<0$
$f^{\prime }\left(x\right)=\frac{1}{1+x^2}-1<0=1-x-x^2<0$
So $x=R-0$