Question

Determine domain of the function $f\left(x\right)=\sqrt{3-2^x-2^{1-x}}+\sqrt{{\sin }^{-1}x}$

• A. $(0,1)$
• B. $(0,2)$
• C. $(-1,1)$
• D. $(-1,0)$

Answer 1

The correct option is A $(0,1)$

Given, $f\left(x\right)=\sqrt{3-2^x-2^{1-x}}+\sqrt{{\sin }^{-1}x}$

${\sin }^{-1}x\ge 0\Rightarrow 0\le x\le 1$

$3-y-\frac{2}{y}\ge 0$ where $y=2^x$ is+iveor $y^2-3y+2\le 0$ or $(y-1)(y-2)\le 0$

$\therefore 1\le y\le 2$ or $2^0\le y\le 2^1$or $2^0\le 2^x\le 2^1$

$\Rightarrow 0\le x\le 1$ as base 2 is greater than

1$\therefore x\in [0,1]$