Problem
ALG-B1-M08-P005 Linear check
#5
★☆☆☆☆ Level 1 of 5
Find all linear functions \(f(x)=ax+b\) such that \(f(x+1)=f(x)+2\) for all \(x\).
Substitute \(ax+b\) and compare the constant parts.
We have \(a(x+1)+b=ax+b+2\). After canceling \(ax+b\), we get \(a=2\). The number \(b\) is arbitrary. Answer: \(f(x)=2x+b\).
Important: this problem is only about linear functions, not all functions.