Question

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

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

Answer 1

Answer: (C)

$\left(-\infty ,\infty \right)$

$f\left(x\right)=co{t}^{-1}x+x$

$f^1\left(x\right)=\frac{-1}{1+x^2+1}$

$=\frac{-1+1+x^2}{1+x^2}$

$=\frac{x^2}{1+x^2}\ge 0$

$f\left(x\right)$ is increasing on $(-\infty ,\infty )$