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JEE Main & Advanced Mathematics Functions Question Bank Functions

  • question_answer
    Let f and g be functions defined by \[f(x)=\frac{x}{x+1},\]\[g(x)=\frac{x}{1-x}\], then \[(fog)(x)\] is         [SCRA 1996]

    A)                    \[\frac{1}{x}\]

    B)            \[\frac{1}{x-1}\]

    C)                    \[x-1\]

    D)            x

    Correct Answer: D

    Solution :

               \[(fog)(x)=f(g(x))=f\left( \frac{x}{1-x} \right)=\frac{\frac{x}{1-x}}{\frac{x}{1-x}+1}=\frac{x}{x+1-x}=x\].


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