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 $\left\{1,(1+\pi {)}^2\right\}$