Vector space help

[Obnoxious]

Is the set of functions: {[math]f® = R |\frac{df}{dx} + 2f = 1[/math]} a vector space? I said no because it doesn't seem to have a zero vector, but I'm doubtful of my answer. Can someone help me prove its vector space validity (or lack thereof)?

[Dave]

I'm not quite sure on my interpretation of your question. Are you asking for all functions f that have a fixed point at R, or the fixed points of the function f, or what?

[Obnoxious]

No, I mean f of a real number is another real number. But I have no idea how to make the funky looking R with Latex

[Tom Mattson]

Are you trying to say the following?

 

[math]\left\{f:\mathbb{R}\rightarrow\mathbb{R}\mid\frac{df}{dx}+2f=1\right\}[/math]

 

If so then you are correct. [imath]f\equiv0[/imath] doesn't satisfy the condition specified in the set definition.

 

No, I mean f of a real number is another real number. But I have no idea how to make the funky looking R with Latex

 

Type the following, without the spaces:

 

[ math ]\mathbb{R}[ \math ]

[Obnoxious]

Yeah, that's what I meant, thanks!