The domain of g alone is x ≠ 0, and the domain of f is all reals. So the domain of (f ◦ g) is the domain of g x . (f ◦ g)(x) = 1/x + 3. The range of g(x) = 1/x is actually the same as its domain y ≠ 0. Adding three, the range of f ◦ g is all reals except for 3, y The line y = 3 is actually an asymptote (horizontal) to the graph of f ◦ g.