MathDB

4

Part of India EGMO 2023 TST

Problems(1)

Identical or Periodic?

Source: India EGMO TST 2023/4

12/10/2022
Let f,gf, g be functions Rā†’R\mathbb{R} \rightarrow \mathbb{R} such that for all reals x,yx,y, f(g(x)+y)=g(x+y)f(g(x) + y) = g(x + y) Prove that either ff is the identity function or gg is periodic.
Proposed by Pranjal Srivastava
algebrafunctionidentityperiodic function