Functions Question 417
Question: The domain and range of the function f given by $ f(x)=2-| x-5 | $ is
Options:
A) $ Domain=,{R^{+}},Range=(-\infty ,1] $
B) $ Domain=,R,Range=(-\infty ,2] $
C) $ Domain=R,Range=(-\infty ,2) $
D) $ Domain ={R^{+}}, Range=(-\infty ,2) $
Show Answer
Answer:
Correct Answer: B
Solution:
[b] Given $ f(x)=2-| x-5 | $ Domain of $ f(x) $ is defined for all real values of x. Since, $ | x-5 |\ge 0\Rightarrow -| x-5 |\le 0 $
$ \Rightarrow 2-| x-5 |\le 2\Rightarrow f(x)\le 2 $ Hence, range of $ f(x) $ is $ ( -\infty ,2 ] $
BETA
