Hello everyone, this is a question about the question number 22. It is in response to the previous here:
http://www.mathematicsgre.com/viewtopic ... 7&hilit=22
gaucho85 says he represents the functions f''(x), f'(x), and f(x) as x^3, x^2, and x respectively. But i don't see how he can do that. If f''(x) is x^3, then f'(x) should be (x^4)/4, and f(x) should be (x^5)/20. Is that right? And if i am wrong i am asking for a little help about why you can assign the f(x) function and its derivatives like that.
Then in the response there is this:
III is the answer since you pick up two functions
h1, h2 satisfy
h1''=h1+1
h2''=h2+1
then (h1+h2)''=h1''+h2''= h1+1+h2+1 =(h1+h2)+2 != (h1+h2)+1
And i think that just because you pick two functions h1 and h2 that both satisfy the equation for choice 3, it doesn't mean that (h1 + h2)'' should equal (h1+h2) +1. Is this right?
So basically i am asking if these two ways of solving the problem are actually correct, because i am a little skeptical. Also i am a little rusty and am trying to study for the GRE, so i would love a little help. Thanks a lot!
Also, there is another post already about this problem and it seems that it contains the best way to solve this problem. You just have to use the fact that for the sets to be subspaces of the real numbers then they must contain the 0 vector and answer 3 does not.
GRE #0658 question #22 rebuttle
Re: GRE #0658 question #22 rebuttle
If the set of real functions satisfying h'' = h + 1 is a subspace of C(R) under addition and scalar multiplication, then by definition it has to be the case that it's closed under addition, i.e., the sum of any two functions which satisfy that differential equation must itself satisfy the equation. The second response you mention, however, shows that this is never the case. Hence it's not a subspace of C(R).
Re: GRE #0658 question #22 rebuttle
Dear,
from where can i have this GRE practice exam.(#0658)
My exam is in october.good luck for all.
from where can i have this GRE practice exam.(#0658)
My exam is in october.good luck for all.

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 Joined: Sun Sep 13, 2009 2:00 pm
Re: GRE #0658 question #22 rebuttle
mag487, thanks for your help. I can see where my problem is, i have to brush up on the properties of these sets. So being closed under addition says that the sum of any two functions must also be on of these functions.
to aas56 go to the GRE website
to aas56 go to the GRE website