Problem
ALG-B3-M11-P001 Unexpected Extra Term
#1
★★★★☆ Level 4 of 5
Let \(f\) be continuous, \(f(x+y)=f(x)+f(y)+4xy\), and \(f(1)=3\). Find \(f\).
Subtract \(2x^2\).
Let \(g(x)=f(x)-2x^2\). Then \(g\) is additive and continuous, so \(g(x)=cx\). From \(f(1)=3\): \(2+c=3\), \(c=1\). The answer is \(f(x)=2x^2+x\).
Warm-up on recognising \(xy\).