Domain of the function f(x) = 2 - 2x - x^2 is - Vidyadip

MCQ

Domain of the function $f(x) = \sqrt {2 - 2x - {x^2}} $ is

A
$ - \sqrt 3 \le x \le \sqrt 3 $
✓
$ - 1 - \sqrt 3 \le x \le - 1 + \sqrt 3 $
C
$ - 2 \le x \le 2$
D
$ - 2 + \sqrt 3 \le x \le - 2 - \sqrt 3 $

✓

Answer

Correct option: B.

$ - 1 - \sqrt 3 \le x \le - 1 + \sqrt 3 $

b
(b) The quantity under root is positive, when

If we want the range of $f(x)$ to be real then, $0 \leq 2-2 x-x^{2}$

$\Longrightarrow x^{2}+2 x \leq 2$

$\Longrightarrow x^{2}+2 x+1 \leq 3$

$\Longrightarrow(x+1)^{2} \leq 3$

$\Longrightarrow-\sqrt{3} \leq x+1 \leq \sqrt{3}$

$\Longrightarrow-\sqrt{3}-1 \leq x \leq \sqrt{3}-1$

So the domain of $x$ is $[-1-\sqrt{3},-1+\sqrt{3}]$

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

JEE STD 11 Science question papers→Gujarat Board STD 11 Science question papers→Gujarat Board question paper generator→

Similar questions

A line is such that its segment between the straight lines $5x - y - 4 = 0$ and $3x + 4y - 4 = 0$ is bisected at the point $(1, 5)$, then its equation is

Last three digits of the number $N = 7^{100} - 3^{100}$ are

If $x = {{2\,t} \over {1 + {t^2}}},\,\,y = {{1 - {t^2}} \over {1 + {t^2}}},$ then ${{d\,y} \over {d\,x}}$ equals

Let $f$ be derivable funciton $f : R\ \rightarrow\ R$ satisfying the equation $f(x) = (1+x^2)\left[ {1 + \int\limits_0^x {\frac{{f(t)}}{{1 + {t^2}}}dt} } \right] $$\forall x \in R$ then $f(1)$ is-

The differential equation of the family of curves represented by the equation ${x^2} + {y^2} = {a^2}$ is

Function $f(x) = {\sin ^{ - 1}}\left( {3x - 4{x^3}} \right)$ is

If straight lines $\alpha^2x + \alpha y = 9$ and $3x + 2y = 5$ are perpendicular, then the value of $\alpha$ is

Let $\vec{a}, \vec{b}$ and $\overrightarrow{ c }$ be three non-coplanar unit vectors such that the angle between every pair of them is $\frac{\pi}{3}$. If $\vec{a} \times \vec{b}+\vec{b} \times \vec{c}=p \vec{a}+q \vec{b}+r \vec{c}$, where $p, q$ and $r$ are scalars, then the value of $\frac{p^2+2 q^2+r^2}{q^2}$ is

If $\alpha, \beta, \gamma, \delta$ are the roots of the equation $x^{4}+x^{3}+x^{2}+x+1=0$, then $\alpha^{2021}+\beta^{2021}+\gamma^{2021}+\delta^{2021}$ is equal to

If the centre of a circle is $(-6, 8)$ and it passes through the origin, then equation to its tangent at the origin, is