Question

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

• A. $[-1,1]$
• B. $(-\infty ,-1)\cup (1,\infty )$
• C. $[-1,\pi +1]$
• D. $(-\infty ,\infty )$

Answer 1

The correct option is A $[-1,1]$

The domain of $\cos x$ is $R$ and the domain of ${\sin }^{-1}x$ is $[-1,1].$
$\therefore$ The domain of ${\sin }^{-1}x+\cos x$ is $R\cap [-1,1]$ i.e., $[-1,1]$