Question

Find the domain and range of the function $f\left(x\right)=2-|x-5|$.

• 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)

$Doman=R,Range=(-\infty ,2]$

Given $f\left(x\right)=2-|x-5|$
Domain of $f\left(x\right)$ is defined for all real values of $x$.
Since, $|x-5|\ge 0⟹-|x-5|\le 0$
$⟹2-|x-5|\le 2⟹f\left(x\right)\le 2$
Hence, range of $f\left(x\right)$ is $(-\infty ,2]$.