Let `f(x)= sin(pi/6sin(pi/2 sin x))` for all `x in R` and `g(x)=pi/2 sinx` for all `x in R` Let `(fog)(x)` denote `f(g(x))` and `(gof)(x)` denote `(g(f(x))`. Then which of the following is (are) true ?

Options

A. Range of `f` is `[-1/2 ,1/2]`
B. Range of `fog` is `[-1/2 ,1/2]`
C. `lim_(xto0) f(x)/g(x)=pi/6`
D. There is an `x in R` such that `(gof)(x)=1`

Answer

A:B:C