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Find the domain of the function f(x) def...

Find the domain of the function `f(x)` defined by `f(x)=sqrt(4-x)+1/(sqrt(x^2-1))` .

A

`(-oo,-1)uu(1,4]`

B

`(-oo,-1]uu(1,4]`

C

`(-oo,-1)uu[1,4]`

D

`(-oo,-1)uu[1,4)`

Text Solution

Verified by Experts

The correct Answer is:
A
We have, `f(x)=sqrt(4-x)+(1)/(sqrt(x^(2)-1))`
f(x) is defined, if `4-xge0orx^(2)-1gt0`
`x-4le0 or (x-1)(x-1)gt0`
`xle4 or xlt-1 and xgt1`
`:.` Domain of `f=(-oo,-1)uu(1,4]`
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