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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] `uu` [ 1, 2]
Now, `y^(2) = 3 + 2 sqrt((3/(2))^(2) - (x^(2) - (5)/(2))^(2)) therefore y_(max)^(2)(x = pm sqrt(5/2)) = 6 y_(min)^(2)(x = pm 1 or pm 2 ) = 3`
Hence range of f(x) is [`sqrt(3) , sqrt(6)]`
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