olymmath

ISL 2012 A5

  • Answer

Find all functions f:R→Rf: \mathbb{R} \rightarrow \mathbb{R} that satisfy the conditions f(1+xy)−f(x+y)=f(x)f(y) for all x,y∈Rf(1+x y)-f(x+y)=f(x) f(y) \text { for all } x, y \in \mathbb{R} and f(−1)≠0f(-1) \neq 0.

Dataset text NuminaMath olympiads. Quoted with source.

Official text: IMO 2012 Shortlist booklet, page 4.

Show the answer

f(x)=x-1, x \in \mathbb{R}

Solutions

Official solution Solution 1 by the IMO Problem Selection Committee

The terms of the source let olymmath link to this solution but not copy it. Read the solution (IMO official site).

Locator isl/2012/a5 · Tag 4HRV4JDYXE · Edit this page on GitHub · Keys: j next, k previous