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JEE Main & Advanced Mathematics Functions Question Bank Functions

  • question_answer
    Let \[g(x)=1+x-[x]\] and \[f(x)=\left\{ \begin{align}   & -1,\,\,\,If\,\,x<0 \\  & \,\,0,\,\,\,If\,\,\,x=0, \\  & \,\,1,\,\,\,\,\,if\,\,\,\,x>0 \\ \end{align} \right.\]then for all values of x the value of \[fog(x)\]                                             [DCE 2005]

    A)                    x

    B)            1

    C)                    \[f(x)\]

    D)             \[g(x)\]

    Correct Answer: B

    Solution :

               \[g(x)=1+\{x\}\]; \[f\{g(x)\}=f\{1+\{x\}\}\]\[=f(k)=1\]                    where, \[k=1+\{x\},1\le k<2\]


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