Functions Question 592
Question: If $ g(f(x))=|\sin x| $ and $ f(g(x))={{(\sin \sqrt{x})}^{2}} $ , then
[IIT 1998]
Options:
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
Show Answer
Answer:
Correct Answer: A
Solution:
$ g,{ f(x) }=,|\sin x|,f{ g(x) }={{(\sin \sqrt{x})}^{2}} $
Considering $ f(x)={{\sin }^{2}}x,g(x)=\sqrt{x}, $ then
$ g,[f(x)]=g,({{\sin }^{2}}x)=\sqrt{{{\sin }^{2}}x}=|\sin x| $
$ f[g(x)]=f[\sqrt{x]}={{(\sin \sqrt{x})}^{2}} $ .
BETA
