# Composite of odd functions is odd

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## Statement

### Statement for two functions

Suppose $f$ and $g$ are odd functions so that the composite $f \circ g$ makes sense. Then, $f \circ g$ is also an odd function.

Note that composition of functions does not commute, so if we can make sense of both $f \circ g$ and $g \circ f$, these are both (possibly equal, possibly distinct) odd functions.

### Statement for more than two functions

Fill this in later