Question

Domain of $f\left(x\right)={\cot }^{-1}x+{\cos }^{-1}x+co{\sec }^{-1}x$ is

• A. $[-1,1]$
• B. $R$
• C. $(-\infty ,-1]\cup [1,\infty )$
• D. $\{-1,1\}$

Answer 1

The correct option is D $\{-1,1\}$

$f\left(x\right)={\cot }^{-1}x+{\cos }^{-1}x+cose{c}^{-1}x$

Domain of ${\cot }^{-1}x=(-\infty ,\infty )$

Domain of ${\cos }^{-1}x=[-1,1]$

Domain of $cose{c}^{-1}x=(-\infty ,-1]\cup [1,\infty )$

These function are in addition.

So, we have to take the intersection of all domains.

So, answer is $\{-1,1\}$

concept: $f\left(x\right)=f_1\left(x\right)+f_2\left(x\right)+...+f_n\left(x\right)$

domain of $f\left(x\right)=$

Domain of $f_1\left(x\right)\cap$ domain of $f_2\left(x\right)$

$\cap$ domain of $f_n\left(x\right)$