Functions Question 717
Question: If $ g(f(x))=| \sin x | $ and $ f(g(x))={{(sin\sqrt{x})}^{2}}, $ then
Options:
A) $ f(x)=sin^{2}x,g(x)=\sqrt{x} $
B) $ f(x)=sinx,g(x)=| x | $
C) $ f(x)=x^{2},g(x)=sin\sqrt{x} $
D) f and g cannot be determined.
Show Answer
Answer:
Correct Answer: A
Solution:
[a] $ g(f(x))=| \sin x | $ indicates that possibly $ f(x)=sinx,g(x)=| x | $ Assuming it correct, $ f(g(x))=f(| x |)sin| x |, $ which is not correct. $ f(g(x))={{( \sin \sqrt{x} )}^{2}} $ indicates that possibly Or $ g(x)=sin\sqrt{x},f(x)=x^{2} $ Then $ g(f(x))=g(sin^{2}x)=\sqrt{\sin x}=| \sin x | $ (For the first combination), which is given. Hence $ f(x)=sin^{2}x,g(x)=\sqrt{x} $
BETA
