Question

Set of values of $x$ for which the function $f\left(x\right)=\frac{1}{x}+2^{{\sin }^{-1}x}+\frac{1}{\sqrt{x-2}}$ exists is

• A. $R$
• B. $R-\left\{0\right\}$
• C. $\varphi$
• D. $R-\left\{1\right\}$

Answer 1

Answer: (C)

$\varphi$

$f\left(x\right)=2{\sin }^{-1}x+\frac{1}{\sqrt{x-2}}+\frac{1}{x}$
$x\ne 0$ for $\frac{1}{x}$
$-1⩽x⩽1$ for ${\sin }^{-1}x$
$\sqrt{x-2}\ne 0$ and $x-2>0$ for $\frac{1}{\sqrt{x-2}}$
$x>2$
n combining, we get domain of $f\left(x\right)$ is $\varphi$.