A) \[f(x)=si{{n}^{2}}x,g(x)=\sqrt{x}\]
B) \[f(x)=sinx,g(x)=\left| x \right|\]
C) \[f(x)={{x}^{2}},g(x)=sin\sqrt{x}\]
D) f and g cannot be determined.
Correct Answer: A
Solution :
[a] \[g(f(x))=\left| \sin x \right|\] indicates that possibly \[f(x)=sinx,g(x)=\left| x \right|\] Assuming it correct, \[f(g(x))=f(\left| x \right|)sin\left| x \right|,\] which is not correct. \[f(g(x))={{\left( \sin \sqrt{x} \right)}^{2}}\] indicates that possibly Or \[g(x)=sin\sqrt{x},f(x)={{x}^{2}}\] Then \[g(f(x))=g(si{{n}^{2}}x)=\sqrt{\sin x}=\left| \sin x \right|\] (For the first combination), which is given. Hence \[f(x)=si{{n}^{2}}x,g(x)=\sqrt{x}\]
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