2. Questions Bank
  3. JEE Main & Advanced
  4. Mathematics
  5. Functions

JEE Main & Advanced Mathematics Functions Question Bank Critical Thinking

  • question_answer
    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

    Correct Answer: A

    Solution :

    • \[g\,\left\{ f(x) \right\}=\,|\sin x|,\,\,f\left\{ g(x) \right\}={{(\sin \sqrt{x})}^{2}}\]           
    • Considering \[f(x)={{\sin }^{2}}x,\,\,g(x)=\sqrt{x},\] then           
    • \[g\,[f(x)]=g\,({{\sin }^{2}}x)=\sqrt{{{\sin }^{2}}x}=\,\,|\sin x|\]                   
    • \[f[g(x)]=f[\sqrt{x]}={{(\sin \sqrt{x})}^{2}}\].


You need to login to perform this action.
You will be redirected in 3 sec spinner