The domain and range of the function f given by f(x) = 2 - x - 5|… - Vidyadip

MCQ

The domain and range of the function $f$ given by $f(x) = 2 - x - 5|$ is.

A
Domain $= R^+, $Range $= ( –\infty, 1)$
✓
Domain $= R,$ Range $= ( –\infty, 2)$
C
Domain $= R,$ Range $= ( –\infty, -2)$
D
Domain$ = R^{+ },$ Range $= ( –\infty, 2)$

✓

Answer

Correct option: B.

Domain $= R,$ Range $= ( –\infty, 2)$

We have$, f(x) = 2 - |x - 5|$
Clearly$, f(x)$ is defined for all $\text{x}\in\text{R}.$
$\therefore$ Domain of $f = R$
Now$, |\text{x}-5|\geq0,\forall\text{x}\in\text{R}$
$\Rightarrow-|\text{x}-5|\leq0$
$\Rightarrow2-|\text{x}-5|\leq2$
$\therefore\text{f(x)}\leq2$
$\therefore$ Range of $\text{f}=(-\infty, 2)$

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 "M.C.Q (1 Marks)" from Relations and Functions→Relations and Functions — all question types→Maths STD 11 Science question papers→CBSE Board STD 11 Science question papers→CBSE Board question paper generator→

Similar questions

The value of $c$, for which the line $y = 2x + c$ is a tangent to the circle ${x^2} + {y^2} = 16$, is

If $p,q,r$ are in $G.P$ and ${\tan ^{ - 1}}p$, ${\tan ^{ - 1}}q,{\tan ^{ - 1}}r$ are in $A.P.$ then $p, q, r$ are satisfies the relation

Permutation relates to the act of arranging all the members of a set into some sequence or order.

The number of integral values of $a$ for which $x^2 -(a -1)x + 3 = 0$ has both roots positive and $x^2 + 3x + 6 -a = 0$ has both roots negative is

The natural number $m$, for which the coefficient of $x$ in the binomial expansion of $\left( x ^{ m }+\frac{1}{ x ^{2}}\right)^{22}$ is $1540,$ is

If ${^\text{m}}\text{C}_{\text{1}}={^\text{n}}\text{C}_{\text{2}},$ is then:

The sum of diameters of the circles that touch $(i)$ the parabola $75 x^{2}=64(5 y-3)$ at the point $\left(\frac{8}{5}, \frac{6}{5}\right)$ and $(ii)$ the $y$-axis, is equal to $......$

$A$ particle is moving in the $x y$-plane along a curve $C$ passing through the point $(3,3)$. The tangent to the curve $C$ at the point $P$ meets the $x$-axis at $Q$. If the $y$-axis bisects the segment $P Q$, then $C$ is a parabola with

$\tan 20^\circ \tan 40^\circ \tan 60^\circ \tan 80^\circ = $

Let $f$ :$ (0, \infty ) \rightarrow R$ & $g$ : $(0,\infty ) \rightarrow R$ be two functions where $g(x) = x + \frac{1}{x}$ . If $1 < f(x).g(x) < 10\,\, \forall x > 0$, then $\mathop {\lim }\limits_{x\, \to \,\infty } f(x)$ is