What Does F Represent in Group Theory?

[MikeDietrich]

Hi-

Let me first start by saying that I do not have a mathematics background and I have a feeling my question is a moronic one but my attempts with "google" did not help so here I am.

I am about to do an assignment (but this is not a homework question IMHO) that asks me to determine if "F", with various operations, are groups. "F" is defined as:

"the set of all real-valued functions of real argument with domain R".

I do not know exactly what this means. In other words, what is "F"? Can someone give some some examples that would fall into set "F"? Or a good link with explanation?

Regards,
Mike

 

[micromass]

In f lie every function of the form $$f:\mathbb{R}\rightarrow \mathbb{R}$$.

Examples:
$$\mathbb{R}\rightarrow \mathbb{R}: x\rightarrow x^2$$
$$\mathbb{R}\rightarrow \mathbb{R}: x\rightarrow x-1$$
$$\mathbb{R}\rightarrow \mathbb{R}: x\rightarrow |x|$$
$$\mathbb{R}\rightarrow \mathbb{R}: x\rightarrow x^5-5x+sin(x)$$

Counterexamples:
$$\mathbb{R}\rightarrow \mathbb{R}: x\rightarrow 1/x$$ (is not defined in 0, so the domain is not entire $$\mathbb{R}$$
$$\mathbb{R}\rightarrow \mathbb{R}: x\rightarrow (x,x)$$ (the element (x,x) is not in the codomain $$\mathbb{R}$$, but in $$\mathbb{R}^2$$).

 

[MikeDietrich]

Perfect. Thank you.