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.