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Question

Let f(x)=x2 and g(x)=sinx for all xR. Then the set of all x satifying (fggf)(x)=(ggf)(x), where (fg)(x)=f(g(x)), is


A

±nπ,n0,1,2,...

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B

±nπ,n1,2,...

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C

π2+2nπ,n...2,1,0,1,2...

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D

2nπ,n...2,1,0,1,2,....

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Solution

The correct option is A

±nπ,n0,1,2,...


Given that f(x)=x2 and g(x)=sinx,xR
Then (gf)(x)=sinx2
(ggf)(x)=sin(sinx2)
As given that (fggf)(x)=(ggf)(x)
sin2(sinx2)=sin(sinx2)sin(sinx2)=0,1
sinx2=nπ or (4n+1)π2 where nZ
sinx2=0sinx2[1,1]x2=nπ
x=±nπ where nW


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