Answer:
Option B
Explanation:
f(x)=x2,g(x)=sinx
(gof)(x)=sinx2
go(gof)(x)=sin(sinx2)
(fogogof)(x)=(sin(sinx2))2.......(i)
Again , (gof)(x)=sinx2
(gogof)(x)=sin(sinx2).....(ii)
Given, (fogogof)(x)=(gogof)(x)
⇒ (sin(sinx2))2=sin(sinx2)
⇒ sin(sinx2)(sin(sinx2)−1)=0
⇒ sin(sinx2)=0 or sin(sinx2)=1
⇒ sinx2=0 or sinx2=π2
∴ x2=nπ
(i.e, not possible as −1≤sinθ≤1)
x=±√nπ