Let `f(x)` be a function such that `f^(prime)(x)=(log)_(1/3)[(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)`

Options

A. `a in (1,4)`
B. `a in (4,oo)`
C. `a in (2,3)`
D. `a in(2,oo)`

Answer

2

Explanation

we must have `log_(1//3) (log_(3)(sin x+a))le0 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`