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:
Keep in mind f(x)=x^n is odd if n is odd and even if n is even.
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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.
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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
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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.
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Cheers,
Stan H.