Question:
The domain and range of real function $t$ defined by $f(x)=\sqrt{x-1}$ is given by
(a) Domain = (1, ∞), Range = (0, ∞)
(b) Domain = [1, ∞), Range =(0, ∞)
(c) Domain = [1, ∞), Range = [0, ∞)
(d) Domain = [1, ∞), Range = [0, ∞)
Solution:
$f(x)=\sqrt{x-1}$
Since x −1 ≥ 0
i.e x ≥ 1
$\therefore$ Domain of $f(x)$ is $[1, \infty)$
and for x∈ [1, ∞)
f(x) ≥ 0
⇒ Range of f(x) is [0, ∞)
Hence, the correct answer is option C.