The domain and range of the function f given by f(x)

f(x) = 2 − |x − 5|

Since f(x) is defined for every x∈R

$\therefore$ Domain is $R$

also |x − 5| ≥ 0

i.e  −|x − 5| ≤ 0

i.e 2 − |x − 5| ≤ 2

$\therefore f(x) \leq 2$

i.e Range for f (x) is (−∞, 2]

Hence, the correct answer is option B.