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Let f(x)=x^2 \ a n d \ g(x)=sinx for all...

Let `f(x)=x^2 \ a n d \ g(x)=sinx` for all `x in R`. Then the set of all `x` satisfying `(fogogof)(x)=(gogof)(x),w h e r e (fog)(x)=f(g(x)),` is

A

`+-sqrt(npi),n epsilon{0,1,2,…………….}`

B

`+-sqrt(npi,n epsilon{1,2,………..}`

C

`(pi)/2+2npi,n epsilon{….-2,-1,0,1,2,………}`

D

`2npi,n epsilon{……….,-2,-1,0,1,2,……..}`

Text Solution

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The correct Answer is:
D
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