Ok so

if f is even and g is even then fog is?

f(x) = f(-x)

g(x) = g(-x)

f(g(x)) = f(g(-x))

f(-g(x)) = f(g(x))

f(-g(x)) = f(-g(-x))

so f(-g(x)) = f(g(x) fog is even???

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- November 26th 2011, 05:09 PMFabio010Even and odd composite functions.
Ok so

if f is even and g is even then fog is?

f(x) = f(-x)

g(x) = g(-x)

f(g(x)) = f(g(-x))

f(-g(x)) = f(g(x))

f(-g(x)) = f(-g(-x))

so f(-g(x)) = f(g(x) fog is even??? - November 26th 2011, 05:57 PMPlatoRe: Even and odd composite functions.
- November 26th 2011, 06:12 PMSorobanRe: Even and odd composite functions.
Hello, Fabio010!

This is simpler than you think . . .

Quote:

We know that: .

The question is: .

Since , we have: . . . . . Yes!

- November 27th 2011, 05:30 AMFabio010Re: Even and odd composite functions.
So if f is odd and g is odd then:

fog is odd because:

f(g(x)) not equal f(-g(x))

since g(-x) = -g(x)

and -f(g(x)) = f(-g(x))

right? - November 27th 2011, 05:39 AMSironRe: Even and odd composite functions.
If is odd then , if is odd then .

Show:

Therefore is odd. - November 27th 2011, 06:38 AMFabio010Re: Even and odd composite functions.
Ok thanks for the help.