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

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

A

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

B

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

C

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

D

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

Text Solution

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The correct Answer is:
A, B, C
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