pow:problem4f24
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| pow:problem4f24 [2024/10/22 03:00] – created mazur | pow:problem4f24 [2024/11/01 03:56] (current) – mazur | ||
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| + | <box 85% round orange|Problem 4 (due on Monday, October 21). > | ||
| + | Find all continuous functions $f:\mathbb R\longrightarrow \mathbb R$ such that for any real numbers $x,y$ | ||
| + | either $f(x+f(y))=f(x)+y$ or $f(f(x)+y)=x+f(y)$. | ||
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| + | </ | ||
| + | The problem was solved by Levi Axelrod and Dr. Mathew Wolak. The only functions which satisfy the conditions | ||
| + | of the problem are $f(x)=x$ and $f(x)=-x$. | ||
| + | Both submitted solution as well as our in-house solution follow the same idea. For details see the following link {{: | ||