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 $(\text{f})=\big[-1-\sqrt{3},-1+\sqrt{3}\big]$

Need a full question paper?

Generate a complete, print-ready paper with questions like this in minutes — across 16+ boards, with answer keys.

Start Generating Free

Explore more

More "MCQ" from RELATIONS AND FUNCTIONS→RELATIONS AND FUNCTIONS — all question types→MATHS STD 11 Science question papers→Gujarat Board STD 11 Science question papers→Gujarat Board question paper generator→

Similar questions

What is the sum of the coefficients of ${({x^2} - x - 1)^{99}}$

If a circle passes through the point $(0, 0), (a, 0), (0, b)$ then its centre is

15 buses operate between Hyderabad and Tirupathi.The number of ways can a man go to Tirupathi from Hyderabad by a bus and return by a different bus is:

Consider the equation $x^2+x-n = 0$, where $n \in N$,and $n \in [5,100].$ Then total Number of different values of $n$, so that the given equation has Integral roots is :-

Let $w=\frac{\sqrt{3}+i}{2}$ and $P=\left\{w^n: n=1,2,3, \ldots\right\}$. Further $H_1=\left\{z \in C: \operatorname{Re} z>\frac{1}{2}\right\}$ and $H_2=\left\{z \in C: \operatorname{Re} z<-\frac{1}{2}\right\}$. where $C$ is the set of all complex numbers. If $z_1 \in P \cap H_1, z_2 \in P \cap H_2$ and $O$ represents the origin, then $\angle z _1 O z _2=$

$(A)$ $\frac{\pi}{2}$ $(B)$ $\frac{\pi}{6}$ $(C)$ $\frac{2 \pi}{3}$ $(D)$ $\frac{5 \pi}{6}$

The locus of the centre of a circle which touches externally the circle $x^2 + y^2 - 6x - 6y + 14 = 0$ $\&$ also touches the $y-$ axis is given by the equation :

Point of intersection of the diagonals of square is at origin and co-ordinate axes are drawn along the diagonals. If the side is of length $'a'$, then one which is not the vertex of square is :-

A circle of constant radius $' a '$ passes through origin $' O '$ and cuts the axes of co-ordinates in points $P$ and $Q$, then the equation of the locus of the foot of perpendicular from $O$ to $PQ $ is :

If $\cot \theta + \tan \theta = 2{\rm{cosec}}\theta $, the general value of $\theta $ is

The equation of the common chord of the circles ${(x - a)^2} + {(y - b)^2} = {c^2}$ and ${(x - b)^2} + {(y - a)^2} = {c^2}$ is