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

The Domain of a function is exactly the set of values that the $x$ can equal.
If the Domain of a $f \left(x\right)$ is ${D}_{f} = \mathbb{R}$, to every $x$ in $\mathbb{R}$, $f \left(x\right)$ is defined.
If the Domain of a $g \left(x\right)$ is ${D}_{g} = \mathbb{R} - \left\{a\right\}$, $g \left(x\right)$ is only defined if $x \ne a$.

The function $f \left(x\right) = \frac{1}{x}$, is not defined for $x = 0$, hence it's Domain equals ${D}_{f} = \mathbb{R} - \left\{0\right\}$.

The function $g \left(x\right) = \ln \left(x\right)$, is not defined for $x \le 0$, hence, it's Domain equals ${D}_{g} = \left\{x \in \mathbb{R} | x > 0\right\}$//

Hope it helps