Additive Function (Conventional)/Examples/3x

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Example of Additive Function

Let $\map f x$ be the real function defined as:

$\forall x \in \R: \map f x = 3 x$

Then $f$ is an additive function.


Proof

\(\displaystyle \map f {x + y}\) \(=\) \(\displaystyle 3 \paren {x + y}\)
\(\displaystyle \) \(=\) \(\displaystyle 3 x + 3 y\)
\(\displaystyle \) \(=\) \(\displaystyle \map f x + \map f y\)

$\blacksquare$


Sources