Which pair of functions have the property that f is O (g) and g is O(f) Answer: (a). f(n) = 2^n and g(n) = 4^n. (b) f(n) = n^3 and g (n) = (n^4 + 3) (n + 5n^2). (c) f(n) = n^6 and g(n) = (n^4 + 3) (n + 5n^2). F(n) = n log n) (4n + 7) and g (n) = n^2. Which pair of values, C and k, are witnesses that show that 2x^2 is O(x^2)? Answer: (a). C = 1, K = 1000 (b). C = 2, k = 100. (c). C = 3, k = 10. (d). C = 4, k = 1