Consider the functions f (x) = 4x and g(x) = x + 6.
(a) Find (f o g) (x).
(b) Find (f o g) 1(x).
(c) Find f −1(x) and g−1(x).
(d) Find (g−1 o f−1) (x) and compare the result with that of part (b).
(e) Repeat parts (a) through (d) for f (x) = x3 + 1 and g(x) = 2x.
(f) Write two one-to-one functions f and g, and repeat parts (a) through (d) for these functions.
(g) Make a conjecture about (f o g) −1(x) and (g−1 o f−1)(x).