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

(B) Domain $=R$, Range $=(-\infty, 2]$
Explanation : We have, $f(x)=2-|x-5|$
Clearly, $f(x)$ is defined for all $x \in R$
$\therefore$ Domain of $f=R$
Now, $|x-5| \geq 0, \forall x \in R$
$\Rightarrow \quad-|x-5| \leq 0$
$\Rightarrow \quad 2-|x-5| \leq 2$
$\therefore f(x) \leq 2$
$\therefore$ Range of $f=(-\infty, 2]$.

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