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CEE Kerala Engineering CEE Kerala Engineering Solved Paper-2009

  • question_answer
    If a function\[f\]satisfies\[f\{f(x)\}=x+1\]for all real values of x and if\[f(0)=\frac{1}{2},\]then\[f(1)\]is equal to

    A)  \[\frac{1}{2}\]                                                  

    B)  1       

    C)  \[\frac{3}{2}\]                  

    D)         2

    E)  0

    Correct Answer: C

    Solution :

    Given,   \[f\{f(x)\}=x+1\]                                      ...(i) \[\therefore \]  \[f(f(0))=0+1\] \[\Rightarrow \]               \[f\left( \frac{1}{2} \right)=1\]                   \[\left[ \because f(0)=\frac{1}{2} \right]\] Now, put\[x=\frac{1}{2}\]in Eq. (i), we get \[f\left\{ f\left( \frac{1}{2} \right) \right\}=\frac{1}{2}+1\]            \[\Rightarrow \]               \[f(1)=\frac{3}{2}\]


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