Problem
ALG-B1-M10-P009 Linear function
#9
★★☆☆☆ Level 2 of 5
Find all linear functions \(f(x)=ax+b\) such that \(f(x+y)=f(x)+f(y)+3\).
Substitute \(ax+b\).
\(a(x+y)+b=ax+b+ay+b+3\). The constants give \(b=2b+3\), so \(b=-3\), while \(a\) is arbitrary. Answer: \(f(x)=ax-3\).
A functional equation in a simple linear class.