Notation Confusion in Linear Transformations

[Offlinedoctor]

I'm just having trouble understanding some of the notations given, when attempting questions such as the following:

{f$\in$F(ℝ,ℝ): f(3)=5}.

Is it just saying that, the function 'f' spans all real values?

 

[HallsofIvy]

I'm just having trouble understanding some of the notations given, when attempting questions such as the following:

{f$\in$F(ℝ,ℝ): f(3)=5}.

Is it just saying that, the function 'f' spans all real values?

That is saying that f is a function from the set of real numbers to the set of real numbers, such that when x= 3, f(x)= 5.

It does NOT necessarily mean that the range of f includes all real numbers, just that the range is some subset of the real numbers.