Problem
ALG-B3-M02-P006 Sum and difference
#6
★★★☆☆ Level 3 of 5
Find all \(f:\mathbb R\to\mathbb R\) such that \(f(x)+f(y)=f(x+y)+f(x-y)\) for all \(x,y\in\mathbb R\).
Hint. Substitute \(y=0\).
With \(y=0\), \(f(x)+f(0)=f(x)+f(x)\), so \(f(x)=f(0)\) for all \(x\). Every constant function works.
Goal: choose the right first substitution and then verify the found function.