Inverse of Linear Function on Real Numbers

Theorem
Let $a, b \in \R$ be real numbers such that $a \ne 0$.

Let $f: \R \to \R$ be the real function defined as:
 * $\forall x \in \R: \map f x = a x + b$

Then the inverse of $f$ is given by:
 * $\forall y \in \R: \map {f^{-1} } y = \dfrac {y - b} a$

Proof
We have that Linear Function on Real Numbers is Bijection.

Let $y = \map f x$.

Then:

and so:
 * $\forall y \in \R: \map {f^{-1} } y = \dfrac {y - b} a$