Need to find if these are true or false. I miss one here and there and can't figure out which.
1.The composition of an even and an odd function is even
2. The ratio of two odd functions is odd
3. The product of two even function is even
4. The composition of an odd function and an odd function is even
5. A function cannot be both even and odd.
6. The sum of two even functions is even
7. The sum of an even and an odd function is usually neither even or odd, but it may be even.
8. The product of two odd function is odd

Question

Need to find if these are true or false. I miss one here and there and can't figure out which.
1.The composition of an even and an odd function is even 
2. The ratio of two odd functions is odd 
3. The product of two even function is even 
4. The composition of an odd function and an odd function is even 
5. A function cannot be both even and odd. 
6. The sum of two even functions is even 
7. The sum of an even and an odd function is usually neither even or odd, but it may be even. 
8. The product of two odd function is odd

amistre64 · Answer

which ones are you missing out on?

anonymous · Answer

That's the thing, I don't know for sure, since my homework will only tell me if I have everything correct, not if I have 1 right here and there. I'll list the answers I have.
T
T
T
T
F
T
F
F

amistre64 · Answer

6 and 7 might need work

the rest seem fine working with the example:

f = x,  is odd
g = x^2, is even

amistre64 · Answer

5 and 7 that is

amistre64 · Answer

f(x) = 0 is even and odd, its symmetric about the origin, and the y axis

anonymous · Answer

That's I figured that one would be true, since 0 is both even and odd. There was even a problem in the homework asking if there is a function that is both even and odd. So I have True for that one.

amistre64 · Answer

f(x) = 0, f(-x) = 0  so  f(x) = f(-x), its even

f(-x) = 0,  -f(x) = 0  so f(-x) = -f(x), its odd

amistre64 · Answer

7 is just too wordy for me

anonymous · Answer

So that one seems to false, right, since it is saying that it cannot be both. That's the answer I had

amistre64 · Answer

ah yes,  wording counts lol

5. A function cannot be both even and odd. 
                   --------

id pick false

anonymous · Answer

Ya, so if everything looks good except the two you mentioned, I tried reversing number 7 but it is saying I still have one wrong.

amistre64 · Answer

1.The composition of an even and an odd function is even 

f(g) = (x)^2 is even,  T

2. The ratio of two odd functions is odd 

f/g = x/x^2 = 1/x,  is odd
g/f = x^2/x = x  is odd,    T

3. The product of two even function is even 

gg= x^2(x^2) = x^4,  T

4. The composition of an odd function and an odd function is even 

f(f) = (x) is odd,  so  F

might be this one

amistre64 · Answer

lets work 7 a little

let f be odd and g be even, and assume their sum can be even

h(x) = f(x)+g(x)

h(-x) = f(-x) + g(-x)
        = -f(x) + g(x)

this is only even if f(-x) = f(x),  but f is odd, and therefore is false by contradiction

anonymous · Answer

So, with your help we get
T
T
T
F
F
T
F
F
?

anonymous · Answer

When I do that it is still wrong =/. I had these type that don't give me a feel for what I did wrong or right. I know most of these, but now I'm questioning everything!

amistre64 · Answer

id go with the last one, but if its saying wrong then im not sure where it would be faulty at

amistre64 · Answer

it would take to long to proof them out, since im losing internet soon

amistre64 · Answer

change 7 to T, just as a guess ... but im at a loss for it

anonymous · Answer

All right, thanks for trying to help any way. Got me on a good track!

amistre64 · Answer

good luck with it ;)