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CEE Kerala Engineering CEE Kerala Engineering Solved Paper-2007

  • question_answer
    Let\[[x]\]denote the greatest integer\[\le x\]. If\[f(x)=[x]\]and\[g(x)=|x|,\]then the value of \[f\left( g\left( \frac{8}{5} \right) \right)-g\left( f\left( -\frac{8}{5} \right) \right)\]is

    A)  2                                            

    B) \[-2\]

    C)  1                            

    D)         0

    E)  \[-1\]

    Correct Answer: E

    Solution :

    Given that,\[f(x)=[x]\]and \[g(x)=|x|\] Now,     \[f\left( g\left( \frac{8}{5} \right) \right)=f\left( \frac{8}{5} \right)=\left[ \frac{8}{5} \right]=1\] and        \[g\left( f\left( -\frac{8}{5} \right) \right)=g\left( \left[ -\frac{8}{5} \right] \right)\]                                 \[=g(-2)=|-2|=2\] \[\therefore \]  \[f\left( g\left( \frac{8}{5} \right) \right)-g\left( \left[ -\frac{8}{5} \right] \right)=1-2=-1\]


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