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    Maths-
    General
    Easy

    Question

    The function f colon R not stretchy rightwards arrow R text  defined by  end text f left parenthesis x right parenthesis equals x minus left square bracket x right square bracket comma straight for all x element of R text  is  end text

    1. one-one
    2. onto
    3. Both one-one and onto
    4. neither one-one nor onto

    Hint:

    In this question, we have to find the type of function if f left parenthesis x right parenthesis equals vertical line x minus 1 vertical line plus vertical line x minus 2 vertical line plus vertical line x minus 3 vertical line comma f colon left square bracket 2 comma 3 right square bracket not stretchy rightwards arrow R A function f colon A rightwards arrow B is said to be one-one if different elements of A have different images in B, a function f colon A rightwards arrow B is said to be onto if for all y element of B, there exists x element of A such that f (x) = y.

    The correct answer is: neither one-one nor onto

      We have f(x)=x-[x].
      Clearly, f(x)=0 for all x element of Z.
      So, f(x) is not one-one function.
      Also, range= [0,1) not equal toR
      So, f(x) is not into function.

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