For a derived varaible f : states → R is strictly decreasing if and only if for states q, q': → f(d) > f(q) → f(d) > f(qg) f(d) < f(q) = f(d) > f(a)

9 c and d

2. Let f (a, b) → R be a function and suppose there exists constants M > 0 and a >1 such that |f(x) = f(y)| ≤ Mx – yª for all x, y € (a, b). Prove or disprove that f is a constant function.

3. Let S {1,2, 3, 4} and define functions f,g : S → S by f = {(1,3), (2,2), (3, 4), (4, 1)} and g = {(1, 4), (2, 3), (3, 1), (4, 2)}. Find (a) g-1 o f og (b) f oglog (c) f-1 og –1 -1ofog