Let x be a variable, and f(x) a function of that variable.
f(2) is a <em>number </em>; it's the value of the function f(x) when x = 2, assuming that value exists.
f(x) = 2 is a <em>statement </em>; it says there is some value of x for which the function returns a value of 2. Because it's a statement, it can be true or false.
Here's an example:
Define f(x) = sin(x). Then f(2) = sin(2) ≈ 0.909297.
If x is a real number, then the statement sin(x) = 2 is false, because -1 ≤ sin(x) ≤ 1 for all real x.
If we replace 2 with 1, on the other hand, we get
f(1) = sin(1) ≈ 0.84147
and
sin(x) = 1 ==> x = π/2 + 2nπ
where n is any integer. (So we're talking about numbers like π/2, -3π/2, 5π/2, -7π/2, and so on.) We're saying here that any real number x of the above form satisfies the equation and makes the statement true.
