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Functions — Maths STD 11 Science — Question

Maharashtra BoardEnglish MediumSTD 11 ScienceMathsFunctions1 Mark
MCQ
The domain of definition of the function $\text{f(x)}=\sqrt{\text{x}-1}+\sqrt{3-\text{x}}$ is :
  • A
    $[1,\infty)$
  • B
    $\big(-\infty,3\big)$
  • C
    $(1,3)$
  • ✓
    $\big[1,3\big]$
✓

Answer

Correct option: D.
$\big[1,3\big]$
$\text{f(x)}=\sqrt{\text{x}-1}+\sqrt{3-\text{x}}$
For $f(x)$ to be defined,
$(\text{x}-1)\geq0$
$\Rightarrow\text{x}\geq1\ ...(\text{i})$
and $(3-\text{x})\geq0$
From $(i)$ and $(ii),$
$\text{x}\in[1,3]$

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