f(x) even, g(x) odd, h(x) = (f*f)(x) + (f*g)(x) + (g*f)(x)

[simonjordan2008]

Suppose that f(x) is an even function, and g(x) is an odd function. Consider the function h(x) = (f ◦ f)(x) + (f ◦ g)(x) + (g ◦ f)(x). Is h(x) odd, even or neither?

 

[jwpaine]

Please show us what you have tried so that we can help!

 

[stapel]

Consider the function h(x) = (f ◦ f)(x) + (f ◦ g)(x) + (g ◦ f)(x).

Do the "dots" indicate multiplication, composition, or something else?

Please include this information when you reply showing all of your work and reasoning so far. Thank you!

Eliz.