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The largest set of real values of x for ...

The largest set of real values of `x` for which `f(x)=sqrt((x + 2)(5-x))-1/sqrt(x^2-4)`- is a real function is

A

`[1,2) cup (2,5]`

B

(2, 5]

C

[3, 4]

D

`[(1)/(sqrt(2)), 1]`

Text Solution

Verified by Experts

The correct Answer is:
B
`f(x) = sqrt((x+2)(5-x)) -(1)/(sqrt(x^(2)-4))`
For f(x) to be real, we have
`(x+2) (5-x) ge 0 and x^(2) -4 gt 0`
i.e. `(x+2) (x-5) le 0 and (x+2)(x-2) gt 0`
Required domain (2, 5)
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