If f and g are real functions and (f+g)(x) is bounded above...

**Mitchell** · October 19th 2009, 09:53 AM

Prove that both f and g are bounded above.

**Defunkt** · October 19th 2009, 09:57 AM

Originally Posted by Mitchell

Prove that both f and g are bounded above.

Let $f,g:\mathbb{R} \to \mathbb{R} : f(x) = x, \ g(x) = -x$

Then, $(f+g)(x) = x + (-x) = 0 \Rightarrow$ (f+g)(x) is bounded above by $M = 0$

But $f(x)$ definitely is not bounded above...

**gmatt** · October 19th 2009, 01:17 PM

The other direction is true, however.

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