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Check continuity and differentibilty of `f(x)=[x]+|1-x|`, [ ] denotes the greatest integer function

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Knowledge Check

  • If f(x)=[sin^(2) x] ([.] denotes the greatest integer function), then

    A
    f is everywhere continuous
    B
    f is everywhere differerntiable
    C
    f is a constant function
    D
    none of these

  • Let f(x)=[|x|] where [.] denotes the greatest integer function, then f'(-1) is

    A
    0
    B
    1
    C
    non-existent
    D
    none of these

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