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) $=(-\infty, 2]$
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