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Even and odd functions

If g(x) is even and h(x) is odd, what is g(h(x))? what about h(g(x))?

Solution Preview

for any x we have g(-x) = g(x) and h(-x) = - h(x) so

g(h(-x)) = g(-h(x)) = g(h(x)) and gh is even;

furthermore,

h(g(-x)) = h(g(x)) and hg is also ...

Solution Summary

This shows how to determine the composition of an even and odd function.

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