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Question

If g{f(x)}=|sin x| and f{g(x)}=(sinx)2, then


A

f(x)=sin2x,g(x)=x

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B

f(x)=sin x,g(x)=|x|

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C

f(x)=x2,g(x)=sinx

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D

f and g cannot be determined

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Solution

The correct option is A

f(x)=sin2x,g(x)=x


Let f(x)=sin2x and g(x)x
Now, fog(x)=f[g(x)]=f(x)=sin2x
and gof(x)=g[f(x)]=g(sin2 x)=sin2x=|sin x|
Again, let f(x)=sin x,g(x)=|x|
fog(x)=f[g(x)]=f(|x|)=sin|x|(sinx)2
When, f(x)=x2,g(x)=sinx
fog(x)=f[g(x)]=f(sinx)=(sinx)2
and (gof)(x)=g[f(x)]=g(x2)=sinx2
=sin|x||sin x|


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