SOLUTION: How do you perform these proofs? i know that for each x in the domain of f, f(x)= f -(x) is an even function odd functions are f(-x) = -f(x) i don't understand how to right

Question 82607: How do you perform these proofs? i know that for each x in the domain of f,
f(x)= f -(x) is an even function
odd functions are f(-x) = -f(x)
i don't understand how to right proofs, although i can solve and find out if a graph is odd or even. these are the questions i had trouble with and couldn't find out how to do it, i'll just type the even questions as they are not in the solution manual:
STATE WHETHER EACH OF THE FOLLOWING IS TRUE OF FALSE:
140) the product of two odd functions is odd
142) the product of an even function and an odd function is odd
actually, i can work out the other one, but the odd one is in the manual, it shows steps, but no explanation:
143) the sum of two even functions is even.
so this question isn't asked, but what about the sum of an even and an odd function?
if this is too many questions, i understand if you can't answer them all, but if you could explain the main concept and maybe take two examples to show me how its down i'd appreciate it. i learn very well once i understand.
thanks, joanna
Answer by stanbon(75887) (Show Source): You can put this solution on YOUR website!
How do you perform these proofs? i know that for each x in the domain of f,
f(x)= f -(x) is an even function
odd functions are f(-x) = -f(x)
i don't understand how to right proofs, although i can solve and find out if a graph is odd or even. these are the questions i had trouble with and couldn't find out how to do it, i'll just type the even questions as they are not in the solution manual:
STATE WHETHER EACH OF THE FOLLOWING IS TRUE OF FALSE:
Keep in mind f(x)=x^n is odd if n is odd and even if n is even.
-------------------
140) the product of two odd functions is odd
But x^3*x^3 is (odd)(odd)= x^6 which is even
So, the product of odds is not always odd; in fact it's always even.
-----------------
142) the product of an even function and an odd function is odd
x^2*x^3= (even)(odd)=x^5 which is odd; the answer is true
---------------------------
actually, i can work out the other one, but the odd one is in the manual, it shows steps, but no explanation:
143) the sum of two even functions is even.
x^2+x^2=2x^2; the answer is true
so this question isn't asked, but what about the sum of an even and an odd function?
if this is too many questions, i understand if you can't answer them all, but if you could explain the main concept and maybe take two examples to show me how its down i'd appreciate it. i learn very well once i understand.
thanks, joanna
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Comment: Examples do not Prove anything; they only illustrate.
Let's just says we don't have room or time for a complete proof here.
=============
Cheers,
Stan H.

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