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$If g [f (x)] = | \sin x | and f [g (x)] = (\sin \sqrt{x})^{2}, then$

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a

f(x)=sin2⁡x,g(x)=x

b

f(x)=sin⁡x,g(x)=|x|

c

f(x)=x2,g(x)=sin⁡x

d

f and g cannot be determined.

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detailed solution

Correct option is A

When f(x)=sin2⁡x and g(x)=x, (fog)(x)=f[g(x)]=f(x)=(sin⁡x)2 and (gof)(x)=g[f(x)]=gsin2⁡x=|sin⁡x| When f(x)=sin⁡x and g(x)=|x| (fog)(x)=f(g(x))=f(|x|)=sin⁡|x|≠(sin⁡x)2 When f(x)=x2 and g(x)=sin⁡x (fog)(x)=f[g(x)]=f(sin⁡x)=(sin⁡x)2 and (gof)(x)=g[f(x)]=gx2=sin⁡x2 =sin⁡|x|≠|sin⁡x|

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