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Find the domain of f(x)=1/(sqrt(|[|x|-1...

Find the domain of `f(x)=1/(sqrt(|[|x|-1]|-5))`

Text Solution

Verified by Experts

The correct Answer is:
`(-oo,-7] cup [7,oo)`
`f(x)=(1)/(sqrt(|[|x|-1]|-5))` is defined. Therefore,
`|[|x|-1]|-5 gt 0`
or `|[|x|-1]| gt 5`
i.e., `[|x|-1] lt -5 " or " [|x|-1] gt 5`
i.e., `|x|-1 lt -5 " or " |x|-1 ge 6`
or `|x| ge 7`
or `x in (-oo,-7] cup [7,oo)`
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