Composite of odd functions is odd

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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

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Related facts

Similar facts

Similar facts for even functions