Odd and even functions proof

[wonderboy]

My teacher asked me as a homework too proove even function/even function=even fuction even fuction/odd function= odd function odd function/even fuction= odd function and odd function/ odd function = even function

 

[burakaltr]

My teacher asked me as a homework too proove even function/even function=even fuction even fuction/odd function= odd function odd function/even fuction= odd function and odd function/ odd function = even function

EVEN f(x) = f(-x) symmetric to y axis

ODD -f(x) = f(-x) symmetric wrt to Origin

even/even ---> f(x)/g(x)

 

[wonderboy]

how would I explain it for other ones

 

[burakaltr]

how would I explain it for other ones

If some function G(x)=f(x)/g(x)

odd/odd

if G(x) even and G(x)=odd/odd where f(x),g(x) are odd

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

G(x)=f(x)/g(x) = -f(-x)/-g(-x)= f(x)/g(x)

G(x) even = -G(x)
etc...