1. The problem statement, all variables and given/known data Let f and g be functions from R to R. For the sum and product of f and g, determine which statements below are true. If true, provide a proof; if false, provide a counterexample. a) If f and g are bounded, then f + g is bounded b) If f and g are founded, then fg is bounded c) If f+g is bounded, then f and g are bounded d) If fg is bounded, then f and g are bounded 2. Relevant equations ? 3. The attempt at a solution "Bounded" just means in the real-numbered set S there is a real number M such that |x|≤M for all x in S. So, say F is the max for f and G is the max for G. For example, say f(x)=5-x2 and g(x)=6-x2. F=5, S=6. f(x) + g(x) = 11-2x2. Still bounded, of course. But how do I give proofs of all these? Give me an example or two.