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BCECE Engineering BCECE Engineering Solved Paper-2012

  • question_answer
    If \[f(x)=\frac{x}{1+|x|}\]for \[x\in R,\]then \[f(0)\]is

    A)  0                                            

    B)         1                            

    C)         2                                            

    D)         does not exist

    Correct Answer: B

    Solution :

    Let \[x<0\Rightarrow |x|=-x\] \[\Rightarrow \]\[f(x)=\frac{d}{dx}\left( \frac{x}{1-x} \right)=\frac{1}{{{(1-x)}^{2}}}\] \[\Rightarrow \]               \[{{[f(x)]}_{x=0}}=1\] Again \[x>0\Rightarrow |x|=x\]                 \[f(x)=\frac{d}{dx}\left( \frac{x}{1+x} \right)\] \[=\frac{1}{{{(1+x)}^{2}}}\]                 \[\Rightarrow \]               \[{{[f(x)]}_{x=0}}=1\]                 \[\Rightarrow \]               \[f(0)=1\]


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