Identity of Affine Group of One Dimension

Theorem
The $1$-dimensional affine group on $\R$ $\operatorname{Af}_1 \left({\R}\right)$ has $f_{1, 0}$ as an identity element.

Proof
Let $f_{ab} \in \operatorname{Af}_1 \left({\R}\right)$.

Then:

Thus $f_{1, 0}$ is the identity element of $\operatorname{Af}_1 \left({\R}\right)$.