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

Let `f(x) = sin (pi/6 sin (pi/2 sinx))` for all `x inR` and `g(x) = pi/2 sinx for all x in R`. Let (fog)(x) dentoe f(g(x)) and (gof)(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 fog is `[-1/2,1/2]`

C

`underset(xrarr0)lim f(x)/g(x) = pi/6`

D

There is an `x inR` such that (gof)(x)=1

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