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Let f(x) = sin ""((pi)/(6) sin""((pi)/...

Let `f(x) = sin ""((pi)/(6) sin""((pi)/(2) sin x ))` for all `x in R and g(x) =(x)/(2) ""sin x` for all ` x in RR` .Let ( fo g) (x) denote f(g(x)) and (go 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

`lim_(x to 0) ""(f(x))/(g(x))=(pi)/(6)`

D

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

Text Solution

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The correct Answer is:
A, B, C
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