Composite of odd functions is odd

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

Related facts

• Composite of even function with odd function is even
• Composite of any function with even function is even