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 − |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.