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JCECE Engineering JCECE Engineering Solved Paper-2003

  • question_answer
    Let \[f(x)\] be defined for all \[x>0\] and be continuous, let \[f(x)\] satisfy\[f\left( \frac{x}{y} \right)=f(x)-f(y)\]for all \[x,\,\,y,\] then:

    A) \[f(x)=\log x\]

    B)  \[f(x)\]is bounded

    C)  \[f\left( \frac{1}{2} \right)\to 0\]as\[x\to 0\]

    D)  \[x\,\,f(x)\to 1\]as\[x\to 0\]

    Correct Answer: A

    Solution :

    Let\[f(x)=\log (x),\,\,x>0\] \[\therefore \]It is continuous for every positive value of\[x\]. \[\therefore \]  \[f\left( \frac{x}{y} \right)=\log \left( \frac{x}{y} \right)=\log (x)-\log (y)\]                             \[=f(x)-f(y)\] \[\therefore \]Option  is correct.


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