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

1.	Find the range of `f(x)sqrt(x-1)+sqrt(5-1)`
Answer» Correct Answer - `[2,2sqrt(2)]` 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)]`.

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