Real Linear Functions
Definition
A real function $f: \R \to \R $ is
linear (a
linear function) if
\[
f(\alpha x + \beta y) = \alpha f(x) + \beta f(y) \quad
\text{for all } x, y, \alpha , \beta \in \R
\]
A real function $f: \R \to \R $ is
linear (a
linear function) if
\[
f(\alpha x + \beta y) = \alpha f(x) + \beta f(y) \quad
\text{for all } x, y, \alpha , \beta \in \R
\]