# Definition:Linearly Dependent Real Functions

## Definition

Let $f \left({x}\right)$ and $g \left({x}\right)$ be real functions defined on a closed interval $\left[{a \,.\,.\, b}\right]$.

Let $f$ and $g$ be constant multiples of each other:

$\exists c \in \R: \forall x \in \left[{a \,.\,.\, b}\right]: f \left({x}\right) = c g \left({x}\right)$

or:

$\exists c \in \R: \forall x \in \left[{a \,.\,.\, b}\right]: g \left({x}\right) = c f \left({x}\right)$

Then $f$ and $g$ are linearly dependent.