Find the range of `f(x)=sqrt(x-1)+sqrt(5-x)`

Answer

`[2,2sqrt(2)]`

Explanation

Let `y=sqrt(x-1)=sqrt(5-x)`
or `y^(2)=x-1+5-x+2 sqrt((x-1)(5-x))`
or `y^(2)=4+2 sqrt(-x^(2)-5+6x)`
or `y^(2)=4+2 sqrt(4-(x-3)^(2))`
then `y^(2)` has minimum value 4 [when `4-(x-3)^(2)=0`] and maximum value 8 when `x=3`.
Therefore, `y in [2,2sqrt(2)]`.