The domain of any step function is the set of all real numbers. The domain deals with the possible inputs for x. We can replace x with any whole number, decimal, fraction, etc and get some output for g(x).
To visually see this, graph g(x) using technology or on graphing paper. Then for every point on the graph, draw a corresponding point straight down or straight up until you reach the x axis. You'll find that the entire x axis gets shaded in to indicate that any x value is allowed.
