Additive Function (Conventional)/Examples/3x

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

\(\ds \map f {x + y}\)

\(=\)

\(\ds 3 \paren {x + y}\)

\(\ds \)

\(=\)

\(\ds 3 x + 3 y\)

\(\ds \)

\(=\)

\(\ds \map f x + \map f y\)

$\blacksquare$

Sources

• 2014: Christopher Clapham and James Nicholson: The Concise Oxford Dictionary of Mathematics (5th ed.) ... (previous) ... (next): additive function