The discussion revolves around finding linear functions that satisfy the identities f[f(x)] = 2x + 1 and f[f[f(x)]] = 2x + 1. Participants are exploring the properties of linear functions in this context.
Some participants have provided hints and initial attempts at solving the first identity, while the second identity remains unaddressed. There is acknowledgment of potential solutions for the first problem, but no consensus on the correctness of these solutions.
Participants note that a and b may not be rational numbers, which introduces complexity into the problem. The original poster has not yet attempted the second identity.
You're give that f(x) is a linear function, so let f(x) = ax + b.SolXero said:Homework Statement
Given f[f(x)] = 2x + 1 find all linear functions that satisfy this identity.
Given f[f[f(x)]] = 2x + 1 find all linear functions that satisfy this identity.
2. The attempt at a solution
I have not started to attempt a solution at this because I have no idea how to do these types of problems.