# The domain and range of real function f defined by

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.