Question

The domain of the function
$f\left(x\right)={\sin }^{-1}\left(\frac{x^2+1}{2x}\right)+\frac{1}{\text{log}\{2-x\}}$
(where $(.)$ denotes the fractional part function) is

• A. $\Phi$ (empty set)
• B. $\{x:x\in I\text{and}x\le 4\}$
• C. $(-\infty ,0)\cup (0,1)$
• D. $\{x:x\in I\text{and}x\ge 3\}$

Answer 1

The correct option is A $\Phi$ (empty set)

Let $g\left(x\right)={\sin }^{-1}\left(\frac{x^2+1}{2x}\right),D_g=\{-1,1\}$
$h\left(x\right)=\frac{1}{\text{log}\{2-x\}},D_h=R-I$
$D_g\cap D_h=\Phi$