Freeflows
Functional Equation Solution 2
Let $ f : \mathbb{R} \to \mathbb{R} $ be a function such that $ f(1) = 1 $ and \[f(x + f(y + z)) + f(f(x + y) + z) = 2y\]for all real numbers $ x, $ $ y, $ and $ z $. Let $ n $ be the number of possible values of $ f(5), $ and let $ s $ be the sum of all possible values of $ f(5) $. Find $ n \times s $.
- 1
- 2
- 3
- +
- 4
- 5
- 6
- -
- 7
- 8
- 9
- $\frac{a}{b}$
- .
- 0
- =
- %
- $a^n$
- $a^{\circ}$
- $a_n$
- $\sqrt{}$
- $\sqrt[n]{}$
- $\pi$
- $\ln{}$
- $\log$
- $\theta$
- $\sin{}$
- $\cos{}$
- $\tan{}$
- $($
- $)$
- $[$
- $]$
- $\cap$
- $\cup$
- $,$
- $\infty$