Very strange. I gave this problem to GPT-3.5 and it answered `f(x)=1/x`. https://www.youtube.com/watch?v=13YrZLBmu7A gives the same solution. GPT-4 failed but was close. Maybe GPT-3.5 is smarter ;)
Query i used was:
```
Can you think step by step about this math problem and solve it?
Let R+ denote the set of positive real numbers. Find all functions f : R+ → R+ such that for each x ∈ R+, there is exactly one y ∈ R+ satisfying xf(y) + yf(x) <= 2.
```
Query i used was: ``` Can you think step by step about this math problem and solve it?
Let R+ denote the set of positive real numbers. Find all functions f : R+ → R+ such that for each x ∈ R+, there is exactly one y ∈ R+ satisfying xf(y) + yf(x) <= 2. ```
Response: https://pastebin.com/sTXM9kLt
Edit: Maybe i should say Bing not GPT-4 because i asked it there.