What does it mean to say a a function f(x) is an element of a particular number?

Question

i.e., say for exmaple, f(x) = 2x - 3,

what does it mean to say that f(x)is an element of {3} or simply f(x)∈{3} ?

I hope the ∈ works.

Answer 1

It means that the value of the function f at x is an element of the set containing only the number 3, so f(x)=3.

For example, if it was R+ instead of {3} with an additional statement "for all x in R" then it would mean that the function only takes on non-negative values for all real numbers.

Answer 2

Seems a little convoluted.

It means that f(x) is an element of the set. Since the set has only one element it means that f(x) = 3. This is only true for one value of x, right?

The set of (x,y) pairs that make f(x) = 2x-3 true is the line. The statement g(x) = 3 is the line (x,3) for any real x. The intersection of those two sets is (3,3), right?

There's a clearer way: f(x) is an element of {3} for some x. Which means there's a value of x such that f(x) =3.