Question

How does the domain of a function relate to its x-values?

Answer 1

The Domain of a function is exactly the set of values that the `x` can equal.
If the Domain of a `f(x)` is `D_(f) = RR`, to every `x` in `RR`, `f(x)` is defined.
If the Domain of a `g(x)` is `D_(g) = RR - {a}`, `g(x)` is only defined if `x!=a`.

The function `f(x) = 1/x`, is not defined for `x = 0`, hence it's Domain equals `D_(f) = RR - {0}`.

The function `g(x)=ln(x)`, is not defined for `x<=0`, hence, it's Domain equals `D_(g) = {x in RR | x>0}`//

Hope it helps