# Math Help - If f and g are real functions and (f+g)(x) is bounded above...

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

Prove that both f and g are bounded above.

2. 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...

3. The other direction is true, however.