Parity of composed functions
Let be an odd function and let be an even function.
What can be said about ?
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1 solution
o ( o ( e ( o ( e ( o ( − x ) ) ) ) ) ) = o ( o ( e ( o ( e ( − o ( x ) ) ) ) ) ) = o ( o ( e ( o ( e ( o ( x ) ) ) ) ) ) therefore the function is even.
It can be done intuitively by considering a negative sign going down through filters (odd functions let it go further but even expel it) so if the composed funtion has at least one even function the hole is even.