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If f(x)=int(0)^(x)log(0.5)((2t-8)/(t-2))...

If `f(x)=int_(0)^(x)log_(0.5)((2t-8)/(t-2))dt`, then the interval in which f(x) is increasing is

A

`(-oo,2)uu(6,oo)`

B

`(4,6)`

C

`(-oo,2)uu(4,oo)`

D

(2,6)

Text Solution

Verified by Experts

The correct Answer is:
B
`f'(x)gt0rArrlog_(0.5)((2x-8)/(x-2))gt0`
`rArr" "(2x-8)/(x-2)lt1`
`rArr" "(2x-8)/(x-2)-1lt0`
`rArr" "x in (2,6)`
Also `(2x-8)/(x-2) gt0 rArr" "x lt 0 or x gt 4`
`rArr" "x in (4,6)`
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