affine functions

[student1234444]

A function f: R → R is called an affine function if a, b ∈ R exist with the following property: ∀x ∈ R: f (x) = ax + b. Let f and g be two bijective affine functions. Show that g ◦ f is also a bijective affine function

 

[blamocur]

From https://www.freemathhelp.com/forum/threads/read-before-posting.109846/:
Show your beginning work, or ask a specific question about the exercise, or explain why you're stuck.

 

[Dr.Peterson]

A function f: R → R is called an affine function if a, b ∈ R exist with the following property: ∀x ∈ R: f (x) = ax + b. Let f and g be two bijective affine functions. Show that g ◦ f is also a bijective affine function

What is required for an affine function to be bijective?

Then, if f(x) = ax + b, and g(x) = cx + d, what is the composition of the functions?