Question

The domain of $f\left(x\right)={\sin }^{-1}\left(\frac{1+x^2}{2x}\right)+\sqrt{\cos \left(\sin x\right)}$ is

• A. $\{-2,2\}$
• B. $\{-1,1\}$
• C. $\{-3,3\}$
• D. $\{0,1\}$

Answer 1

Answer: (B)

$\{-1,1\}$

$f\left(x\right)={\sin }^{-1}\left(\frac{1+x^2}{2x}\right)+\sqrt{\cos \left(\sin x\right)}$
Function is defined for $-1\le \frac{1+x^2}{2x}\le 1$ and $\cos \left(\sin x\right)\ge 0$
$1+x^2+2x=0$ and $1+x^2-2x=0$
$\Rightarrow (1+x{)}^2\ge 0$and $\Rightarrow (1-x{)}^2\le 0$
$\Rightarrow x=-1,1$ and $\cos \left(\sin x\right)\ge 0$ is also satisfied by $-1,1$
Then, the domain of function is $-1,1$