Determine whether the following are Vector Spaces

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Homework Statement



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]

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.
 

Answers and Replies

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

What about 5f(x)?
 

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