To find the range of $\sqrt{x-1} + \sqrt{5-x}$ To find the range of $\sqrt{x-1} + \sqrt{5-x}$.
I do not know how to start?
Thanks

Clearly $1\le x\le5$
If $y=\sqrt{x-1}+\sqrt{5-x}>0, y^2=4+2\sqrt{(x-1)(5-x)}$
Now $\sqrt{(x-1)(5-x)}\ge0$
and using AM-GM inequality, $\sqrt{(x-1)(5-x)}\le\dfrac{x-1+5-x}2=?$
