If \[g(f(x))=|\sin x|\] and \[f(g(x))={{(\sin \sqrt{x})}^{2}}\], then [IIT 1998]

\[f(x)={{\sin }^{2}}x,\ g(x)=\sqrt{x}\]

\[f(x)={{x}^{2}},\ g(x)=\sin \sqrt{x}\]

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

1.	If \[g(f(x))=\|\sin x\|\] and \[f(g(x))={{(\sin \sqrt{x})}^{2}}\], then [IIT 1998]
A.	\[f(x)={{\sin }^{2}}x,\ g(x)=\sqrt{x}\]
B.	\[f(x)=\sin x,\ g(x)=\|x\|\]
C.	\[f(x)={{x}^{2}},\ g(x)=\sin \sqrt{x}\]
D.	f and g cannot be determined
Answer» B. \[f(x)=\sin x,\ g(x)=\|x\|\]

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If \[g(f(x))=|\sin x|\] and \[f(g(x))={{(\sin \sqrt{x})}^{2}}\], then [IIT 1998]

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