Question

The domain of the function $f\left(X\right)=\sqrt{3-2^x-2^{1-x}}+\sqrt{si{n}^{-1}x}$ is

• A. [-1, 0]
• B. [0, 1]
• C. $[\frac{1}{2},1]$
• D. [1,2]

Answer 1

The correct option is B [0, 1]

$si{n}^{-1}x\ge 0\Rightarrow 0\le x\le 1$
and $2^x+2^{1-x}\le 3\Rightarrow 2^x+{2.2}^{-x}-3\le 0$
Put $2^x=t$, then $t^2-3t+2\le 0\Rightarrow (t-2)(t-1)\le 0$
$\Rightarrow 1\le t\le 2$ i.e $1\le 2^x\le 2$
$\Rightarrow 0\le x\le 1$