MCQ
The domain and range of $f(x)=2-|x-5|$ are
- A$R+,(-\infty, 1]$
- ✓$R,(-\infty, 2]$
- C$R,(-\infty, 2)$
- D$R+,(-\infty, 2]$
✓
Answer
Correct option: B.
$R,(-\infty, 2]$
(B) $R_t(-\infty, 2]$
Hint:
$f(x)=2-|x-5| $
$=2-(5-x), x<5$
$=2-(x-5), x \geq 5 $
$\therefore f(x)=x-3, x<5 $
$=7-x, x \geq 5$
Domain $=R$,
Range (from graph) $=(-\infty, 2]$
Hint:
$f(x)=2-|x-5| $
$=2-(5-x), x<5$
$=2-(x-5), x \geq 5 $
$\therefore f(x)=x-3, x<5 $
$=7-x, x \geq 5$
Domain $=R$,
Range (from graph) $=(-\infty, 2]$
Need a full question paper?
Generate a complete, print-ready paper with questions like this in minutes — across 16+ boards, with answer keys.
Explore more
Similar questions
If the coefficients of $x^2$ and $x^3$ in the expansion of $(3+a x)^9$ are the same, then the value of a is
→The number of real values of $\lambda$ for which the lines $\text{x} - 2\text{y} + 3 = 0, \lambda\text{x} + 3\text{y} + 1 = 0$ and $4\text{x} - \lambda\text{y} + 2 = 0$ are concurrent is :
→Let $D=\left|\begin{array}{ccc}\sin \theta \cdot \cos \phi & \sin \theta \cdot \sin \phi & \cos \theta \\ \cos \theta \cdot \cos \phi & \cos \theta \cdot \sin \phi & -\sin \theta \\ -\sin \theta \cdot \sin \phi & \sin \theta \cdot \cos \phi & 0\end{array}\right|$ then
→The equation of a line, whose perpendicular distance from the origin is 5 units and the angle, which is perpendicular to the line from the origin makes, is $210^{\circ}$ with positive $X$-axis, is
→A parabola has the origin as its focus and the line $x=2$ as the directrix. Then the vertex of the parabola is at
→Two dice are thrown together. The probability that neither they show equal digits nor the sum of their digits is $9$ will be :
→If in a regular polygon, the number of diagonals are 54 , then the number of sides of the polygon are
If $\omega$ is a complex cube root of unity, then the value of $\omega^{99}+\omega^{100}+\omega^{101}$ is
→The difference of the focal distance of any point on the hyperbola $9 x^2-16 y^2=144$, is
→If $e_1$ is the eccentricity of the conic $9x^2 + 4y^2 = 36$ and $e_2$ is the eccentricity of the conic $9x^2 − 4y^2 = 36,$ then
→