Comment: Here we consider $g(x) = 2x +5$ and the domain is $\{x : 2x+5 >0\} = (-2.5, \infty)$.

The mapping diagram visualizes $h$ as a composition which shows how the domain of $h$ is determined by the domain of $\log_b$.

The GeoGebra mapping diagram can be used to visualize the domain for other compositions where $h(x)=f(g(x))=\log_b(g(x))$ .

Try $g(x)=|x|, g(x)=x^2−4$ and $g(x)=4−x^2$.