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

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

(a) Domain = R+, Range = (−∞, 1]

(b) Domain = R, Range = (−∞, 2]

(c) Domain =R, Range = (−∞, 2)

(d) Domain = R+, Range = (−∞, 2]

Solution:

f(x) = 2 − |− 5|

Since f(x) is defined for every xR

$\therefore$ Domain is $R$

also |− 5| ≥ 0

i.e  −|− 5| ≤ 0

i.e 2 − |− 5| ≤ 2

$\therefore f(x) \leq 2$

i.e Range for (x) is (−∞, 2]

Hence, the correct answer is option B.