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| \geq 0 $
$\Rightarrow -|x-5| \leq 0$
$\Rightarrow 2-|x-5| \leq 2$
$ \Rightarrow f(x) \leq 2$
Hence, range of $f ( x )$ is $(-\infty, 2]$.