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Let f(x)=sin(pi/6sin(pi/2sinx)) for all ...

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

A

Range of f is `[-1/2,1/2]`

B

Range of `f o g` is `[-1/2,1/2]`

C

`underset(x rarr 0) lim f(x)/g(x)=pi/6`

D

There is an `x in RR` such that `(g o f)(x)=1`

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