## A Group of Linear Functions

## Problem 6

Define the functions $f_{a,b}(x)=ax+b$, where $a, b \in \R$ and $a>0$.

Show that $G:=\{ f_{a,b} \mid a, b \in \R, a>0\}$ is a group . The group operation is function composition.

Add to solve laterDefine the functions $f_{a,b}(x)=ax+b$, where $a, b \in \R$ and $a>0$.

Show that $G:=\{ f_{a,b} \mid a, b \in \R, a>0\}$ is a group . The group operation is function composition.

Add to solve laterLet $G$ and $G’$ be a group and let $\phi:G \to G’$ be a group homomorphism.

Show that $\phi$ induces an injective homomorphism from $G/\ker{\phi} \to G’$.

Add to solve later