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Let `f(x)` be a function such that `f(x)=(log)_(1/2)[(log)_3(sinx+a]dot` If `f(x)` is decreasing for all real values of `x ,` then `a in (1,4)` (b) `a in (4,oo)` `a in (2,3)` (d) `a in (2,oo)`

A

`a in (1,4)`

B

`a in (4,oo)`

C

`a in (2,3)`

D

`a in(2,oo)`

Text Solution

Verified by Experts

The correct Answer is:
2
we must have `log_(1//3) (log_(3)(sin x+a))le0 forall 0 forall x In R`
or `log_(3)(sinx+a)gt forall x in R`
or ` sin x + a le 3 forall x in R`
or `age 3-sin x forall x in R`
or `age4`
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