Question

Let $f\left(x\right)={\sec }^{-1}x+{\tan }^{-1}x.$ Then $f\left(x\right)$ is real for

• A. $xϵ[-1,1]$
• B. $xϵR$
• C. $xϵ(-\infty ,-1]\cup [1,+\infty )$
• D. none of these

Answer 1

The correct option is C $xϵ(-\infty ,-1]\cup [1,+\infty )$

The domain of ${\sec }^{-1}\left(x\right)$ is $(-\infty ,-1]\cup [1,\infty )$
And the domain of ${\tan }^{-1}\left(x\right)$ is $(-\infty ,\infty )$
Hence, $f\left(x\right)$ is define for $xϵ(-\infty ,-1]\cup [1,\infty )$.