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Relations and Functions — Maths STD 11 Science — Question

CBSE BoardEnglish MediumSTD 11 ScienceMathsRelations and Functions1 Mark
MCQ
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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