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

Let `f(x)=sin((pi)/(6)sin((pi)/(2)sinx)) " 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?

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

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

`lim_(xto0)(g(x))/(g(x))=(pi)/6`

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

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A, B, C

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