MCQ
The domain of the function $f(x)=\sqrt{x-1}+\sqrt{6-x}$
- A$(-\infty, 6)$
- B$[2,6]$
- ✓$[1,6]$
- D$[-2,6]$
✓
Answer
Correct option: C.
$[1,6]$
For $f(x)$ to be real, we must have,
$x-1 \geqslant 0 \text { and } 6-x \geqslant 0$
$\Rightarrow x \geqslant \varphi \text { and } x-6 \leqslant 6$
$\therefore \text { Domain }=[1,6]$
$x-1 \geqslant 0 \text { and } 6-x \geqslant 0$
$\Rightarrow x \geqslant \varphi \text { and } x-6 \leqslant 6$
$\therefore \text { Domain }=[1,6]$
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