Let f, g: Z+ → Z+ where for all x e Z+, f(x) = x + 1 and g(x) = max{l, x - 1}, the maximum of 1 and x - f.
(a) What is the range of /?
(b) Is f an onto function?
(c) Is the function f one-to-one?
(d) What is the range of g?
(e) Is g an onto function?
(f) Is the function g one-to-one?
(g) Show that go f = lz+.
(h) Determine (f o g)(x) for x = 2, 3, 4, 7, 12, and 25.
(i) Do the answers for parts (b), (g), and (h) contradict the result in Theorem 5.8?