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KVPY Sample Paper KVPY Stream-SX Model Paper-6

  • question_answer
    Let f & g be two functions defined as follows; \[f\,(x)=\frac{x+|x|}{2}\] for all x & \[g\,(x)=\left[ \begin{matrix}    x & \text{for} & x<0  \\    {{x}^{2}} & \text{for} & x\ge 0  \\ \end{matrix} \right.\] then:

    A) (gof)(x) & (fog)(x) are both cont. for all \[x\in R\]

    B) (gof)(x) & (fog)(x) are unequal functions

    C) (got) is non-differentiable at \[x=0\]

    D) (fog)(x) is not differentiable at \[x=0.\]

    Correct Answer: A

    Solution :

    \[g\,[f\,(x)]=f\,[g\,(x)]=\left[ \begin{matrix}    {{x}^{2}} & \text{if} & x\ge 0  \\    0 & \text{if} & x<0  \\ \end{matrix} \right.\]


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