Question

Find the domain of the function $f\left(x\right)=\sqrt{x-1}+\sqrt{7-x}$

Answer 1

Let $f_1\left(x\right)=\sqrt{x-1}\Rightarrow D_1=x\ge 1$

$f_2\left(x\right)=\sqrt{7-x}\Rightarrow D_2=7-x\ge 0\Rightarrow x\le 7$

Domain of $f\left(x\right)=D_1\cap D_2=[1,7]$