1.

if `|(2)/(x-4)| gt 1`, then x belongs to the internalA. `(2, 6)`B. `(2, 4) cup (4, 6)`C. `(-oo, 2)`D. `(6, oo)`

Answer» Correct Answer - B
We have,
`|(2)/(x-4)| gt 1`
`rArr (2)/(|x-4|) gt 1`
`rArr 2 gt |x-4|`
` rArr |x-4| lt 2`
`rArr 4-2 lt x lt 4+2 " " [because |x-a| lt r hArr a-r lt x lt a+r]`
`rArr 2 lt x lt 6`
`"But", (2)/(x-4)` is not meaningful for x = 4.
`therefore 2 lt x lt 6 " and " x ne 4 rArr x in (2, 4)cup(4,6)`


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