Question

F (x) = x + 3; g(x) = 1/x What is the domain and range of (f • g)

Answer 1

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