Question

The function $f(x)=co{t}^{-1}x+x$ increases in the interval

• A. $\left(1,\infty \right)$
• B. $\left(-1,\infty \right)$
• C. $\left(0,\infty \right)$
• D. $\left(-\infty ,\infty \right)$

Answer 1

Answer: (D)

$f\left(x\right)=co{t}^{-1}x+x$
$\Rightarrow f^{\prime }\left(x\right)=\frac{-1}{1+x^2}+1$
$\Rightarrow f^{\prime }\left(x\right)=\frac{x^2}{1+x^2}\ge 0$,
for $x\in R$
$\therefore f\left(x\right)$ is increasing on $\left(-\infty ,\infty \right)$.