Question

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

• A. Doman $=R^{+}$, Range $=(-\infty ,1]$
• B. Doman $=R$, Range $=(-\infty ,2]$
• C. Doman $=R$, Range $=(-\infty ,2)$
• D. Doman $=R^{+}$, Range $=(-\infty ,2]$

Answer 1

Answer: (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 $(-\infty ,2]$.