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Homework Help: Determine whether the following are Vector Spaces

  1. Apr 10, 2013 #1
    1. The problem statement, all variables and given/known data

    a) The set of real polynomials of [itex]x[/itex] divisible by [itex]x^2 + x + 1[/itex];
    b) The set of differentiable functions of [itex]x[/itex] on [itex][0,1][/itex] whose derivative is [itex]3x^2[/itex]
    c) all [itex]f \in F[0,2][/itex] such that [itex]x \geq |f(x)|[/itex] for [itex]0 \leq x \leq 2[/itex]

    3. The attempt at a solution

    a) Yes, it's a vector space, proven with addition and scalar multiplication

    b) I don't really understand what the question is saying, can someone explain to me? A function that differentiates to [itex]3x^2[/itex] is [itex]x^3[/itex]. Now what?

    c) Same goes for this part, not sure what the question is saying

    Thanks in advanced.
  2. jcsd
  3. Apr 10, 2013 #2

    Simon Bridge

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    (b) That is not all the functions that differentiate to ##3x^2##
    (c) Try telling us what you think it's saying so we can see where the confusion lies.
  4. Apr 11, 2013 #3


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    f(x)= (2/3)x has the property that x> |f(x)|.

    What about 5f(x)?
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