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RAJASTHAN ­ PET Rajasthan PET Solved Paper-2012

  • question_answer
    If\[f(x)=\frac{{{4}^{x}}}{{{4}^{x}}+2},\]then \[f\left( \frac{1}{97} \right)+f\left( \frac{2}{97} \right)+....+f\left( \frac{96}{97} \right)\] is equal to

    A)  1            

    B)  48

    C)  \[-48\]         

    D)  \[-1\]

    Correct Answer: B

    Solution :

    Since,  \[f(x)=\frac{{{4}^{x}}}{{{4}^{x}}+2}\] \[\therefore \] \[f(1-x)=\frac{{{4}^{1-x}}}{{{4}^{1-x}}+2}\] \[=\frac{4}{4+{{2.4}^{x}}}=\frac{2}{2+{{4}^{x}}}\] \[\Rightarrow \] \[f(x)+f(1-x)=1\] On putting\[x=\frac{1}{97},\frac{2}{97},.....,\frac{48}{97},\]we get \[f\left( \frac{1}{97} \right)+f\left( \frac{2}{97} \right)+....+f\left( \frac{96}{97} \right)=48\]


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