# Determine whether the following are Vector Spaces

1. Apr 10, 2013

### Smazmbazm

1. The problem statement, all variables and given/known data

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

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 $3x^2$ is $x^3$. Now what?

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

2. Apr 10, 2013

### Simon Bridge

(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. Apr 11, 2013

### HallsofIvy

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