Question

If f is an odd function and g is an even function, show that the composite functions f ◦ g and g ◦ f are both even.

Answer 1

do you know what it is you have to show?

Answer 2

just explain that it is true

Answer 3

no you have to work directly from the definition of "even"
do you know what it means for a function to be "even"?

Answer 4

\[E(x)\] is even means \(E(x)=E(-x)\)

Answer 5

so exactly what you have to show is that
\[f\circ g(-x)=f\circ g(x)\] and
\[g\circ f(-x)=g\circ f(x)\]

Answer 6

for the one way

\((f\circ g)(-x)=f(g(-x)=f(g(x)) = (f\circ g)(x)\)

you try the other way