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The range of the function f(x) = sqrt(4...

The range of the function ` f(x) = sqrt(4 - x^2) + sqrt(x^2 - 1)` is

A

`[sqrt(3), sqrt(7)]`

B

`[sqrt(3), sqrt(5)]`

C

`[sqrt(2), sqrt(3)]`

D

`[sqrt(3),sqrt(6)]`

Text Solution

Verified by Experts

The correct Answer is:
D
`Let y = f(x) = sqrt(4-x^(2)) + sqrt(x^(2) -1)`
Clearly domain of f(x) is `[-2,-1] cup [1,2]`
Now , `y^(2) = 3 + 2 sqrt(((3)/(2))^(2) - (x^2 - (5)/(2))^(2)) :. y_(max)^(2) ( x = pm sqrt(5)/2) = 6 and y_("min")^(2) ( x = pm 1 or pm 2 ) =3`
Hence range of f(x) is `[sqrt(3) , sqrt(6)] `
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