Thread: Even 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???

Originally Posted by fabio010

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???

correct.

Hello, Fabio010!

This is simpler than you think . . .

We know that: .

The question is: .


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

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?

If is odd then , if is odd then .

Show:


Therefore is odd.

Ok thanks for the help.