The domain of the function $f(x)=\sqrt{x-1}+\sqrt{6-x}$ is
The domain of the function $f(x)=\sqrt{x-1}+\sqrt{6-x}$ is
$[1, \infty)$
$[1,6]$
$(-\infty, 6]$
$(-\infty, 6)$
Solution
$f(x)=\sqrt{x-1}+\sqrt{6-x}$
Here $\mathrm{f}(\mathrm{x})$ is defined when
$x-1 \geq 0$ and $6-x \geq 0 \quad$ i.e.
$x \geq 1$ and $x-6 \leq 0 \quad$ i.e. $x \geq 1$ and $x \leq 6$
$\therefore$ Domain of $\mathrm{f}(\mathrm{x})$ is $[1,6]$