Prove that both f and g are bounded above.
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Originally Posted by Mitchell Prove that both f and g are bounded above. Let $\displaystyle f,g:\mathbb{R} \to \mathbb{R} : f(x) = x, \ g(x) = -x$ Then, $\displaystyle (f+g)(x) = x + (-x) = 0 \Rightarrow$ (f+g)(x) is bounded above by $\displaystyle M = 0$ But $\displaystyle f(x)$ definitely is not bounded above...
The other direction is true, however.
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