(adsbygoogle = window.adsbygoogle || []).push({}); 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

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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-x^{2}and g(x)=6-x^{2}. F=5, S=6.

f(x) + g(x) = 11-2x^{2}.

Still bounded, of course. But how do I give proofs of all these? Give me an example or two.

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# Homework Help: One more H.W. question

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