The domain of the function f(x)= 2-2x-x^2 is: - Vidyadip

MCQ

The domain of the function $\text{f(x)}=\sqrt{2-2\text{x}-\text{x}^2}$ is:

A
$\big[-\sqrt{3},\sqrt{3}\big]$
✓
$\big[-1,-\sqrt{3},-1+\sqrt{3}\big]$
C
$\big[-2,2\big]$
D
$\big[-2-\sqrt{3},-2+\sqrt{3}\big]$

✓

Answer

Correct option: B.

$\big[-1,-\sqrt{3},-1+\sqrt{3}\big]$

$\text{f(x)}=\sqrt{2-2\text{x}-\text{x}^2}$
Since, $2-2\text{x}-\text{x}^2\geq0$
$\text{x}^2+2\text{x}-2\leq0$
$\Rightarrow\text{x}^2-2\text{x}-2+1-1\leq0$
$\Rightarrow(\text{x}-1)^2-\big(\sqrt{3}\big)^2\leq0$
$\Rightarrow\big[\text{x}-\big(1-\sqrt{3}\big)\big]\big[\text{x}-\big(1+\sqrt{3}\big)\big]\leq0$
$\Rightarrow\big(-1-\sqrt{3}\big)\leq\text{x}\leq(-1+\sqrt{3})$
Thus, domain $(\text{f})=\big[-1-\sqrt{3},-1+\sqrt{3}\big]$

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