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

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

Text Solution

Verified by Experts

The correct Answer is:
`[2,2sqrt(2)]`
Let `y = sqrt(x - 1) + sqrt(5 -x)`
`rArr y^(2) = x - 1 + 5 - x + 2 sqrt((x - 1)(5 - x))`
`= 4 + 2 sqrt(-x^(2)-5 +6x)`
`= 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. They, y `in[2,2,sqrt(2)]` .
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