Question

The range of the function, $f(x)=\left(1+\sec ^{-1} x\right)\left(1+\cos ^{-1} x\right)$ is

• A. $(-\infty, \infty)$
• B. $(-\infty, 0] \cup[4, \infty) $
• C. $\left\{1,(1+\pi)^2\right\}$
• D. $\left[0,(1+\pi)^2\right]$

Answer 1

Answer: (C)

$f$ is defined only for $x =1$ and -1
$\therefore f (1)=1 ; f (-1)=(1+\pi)(1+\pi)=(1+\pi)^2$
range is $\left\{1,(1+\pi)^2\right\}$