Choose the correct answers:The domain and range of real function … - Vidyadip

MCQ

Choose the correct answers:The domain and range of real function f defined by $\text{f(x)}=\sqrt{\text{x}-1}$ is given by.

✓
Domain $= [1, \infty),$ Range $= [0, \infty)$
B
Domain $= [1, \infty),$ Range $= [0, \infty)$
C
Domain $= [1, \infty),$ Range $= [0, \infty)$
D
Domain $= [1, \infty),$ Range $= [0, \infty)$

✓

Answer

Correct option: A.

Domain $= [1, \infty),$ Range $= [0, \infty)$

We have, $\text{f(x)}=\sqrt{\text{x}-1}$
Clearly, $f(x)$ is defined if $\text{x}-1\geq0$
$\Rightarrow\text{x}\geq1$
$\therefore$ Domain of $\text{f}=[1, \infty)$
Now for $\text{x}\geq1,\text{x}-1\geq0$
$\Rightarrow\sqrt{\text{x}-1}\geq1$
$\Rightarrow$ Range of $= [0, \infty)$

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