(a) Use properties of quadratic functions to prove that (x 1)2 <3x for all real x 2. (b) Use mathematical induction and the inequality

(a) Use properties of quadratic functions to prove that (x 1)2 2. (c) Let g(n) = 5+1 + (n-1) and h(n) = 6". Using the inequality from part (b), prove that g(n) = O(h(n)). You need to give a rigorous proof derived directly from the definition of the O- notation, without using any theorems from class. (First, give a complete statement of the definition. Next, show how g(n) = O(h(n)) follows from this definition.)