document.write( "<A HREF=/cgi-bin/jump-to-question.mpl?question=82607>Question 82607</A>: <I><SPAN STYLE=\"word-break: break-all;\"> How do you perform these proofs?  i know that for each x in the domain of f, <BR>\n" );
document.write( "f(x)= f -(x) is an even function<BR>\n" );
document.write( "odd functions are f(-x) = -f(x)\r<BR>\n" );
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document.write( "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:\r<BR>\n" );
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document.write( "STATE WHETHER EACH OF THE FOLLOWING IS TRUE OF FALSE:\r<BR>\n" );
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document.write( "140) the product of two odd functions is odd<BR>\n" );
document.write( "142) the product of an even function and an odd function is odd<BR>\n" );
document.write( "actually, i can work out the other one, but the odd one is in the manual, it shows steps, but no explanation:<BR>\n" );
document.write( "143) the sum of two even functions is even.<BR>\n" );
document.write( "so this question isn't asked, but what about the sum of an even and an odd function?\r<BR>\n" );
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document.write( "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.\r<BR>\n" );
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document.write( "thanks, joanna </SPAN>\n" );
document.write( "</I><HR><TABLE width=100%><TR><TD><B><A HREF=http://www.algebra.com/>Algebra.Com's</A> Answer #59204 by </B><A HREF=/tutors/aboutme.mpl?userid=stanbon><B>stanbon(75887)</B></A><img src=\"/images/stars/stars-13.gif\" alt=\"\" >&nbsp;<A HREF=/tutors/aboutme.mpl?userid=stanbon><IMG SRC=http://www.algebra.com/images/aboutme-small.gif BORDER=0 alt=\"About Me\" VALIGN=MIDDLE></A>&nbsp;<IMG SRC=http://www.algebra.com/images/nopicture.jpg><BR>You can <A HREF=\"/cgi-bin/embed-solution.mpl?show=1&solution=59204\">put this solution on YOUR website!</A><BR><SPAN STYLE=\"word-break: break-all;\"> How do you perform these proofs? i know that for each x in the domain of f, <BR>\n" );
document.write( "f(x)= f -(x) is an even function<BR>\n" );
document.write( "odd functions are f(-x) = -f(x) <BR>\n" );
document.write( "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: <BR>\n" );
document.write( "STATE WHETHER EACH OF THE FOLLOWING IS TRUE OF FALSE:<BR>\n" );
document.write( "Keep in mind f(x)=x^n is odd if n is odd and even if n is even.<BR>\n" );
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document.write( "140) the product of two odd functions is odd<BR>\n" );
document.write( "But x^3*x^3 is (odd)(odd)= x^6 which is even<BR>\n" );
document.write( "So, the product of odds is not always odd; in fact it's always even.<BR>\n" );
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document.write( "142) the product of an even function and an odd function is odd<BR>\n" );
document.write( "x^2*x^3= (even)(odd)=x^5 which is odd; the answer is true<BR>\n" );
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document.write( "actually, i can work out the other one, but the odd one is in the manual, it shows steps, but no explanation:<BR>\n" );
document.write( "143) the sum of two even functions is even.<BR>\n" );
document.write( "x^2+x^2=2x^2; the answer is true<BR>\n" );
document.write( "so this question isn't asked, but what about the sum of an even and an odd function? <BR>\n" );
document.write( "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. <BR>\n" );
document.write( "thanks, joanna<BR>\n" );
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document.write( "Comment: Examples do not Prove anything; they only illustrate.<BR>\n" );
document.write( "Let's just says we don't have room or time for a complete proof here.<BR>\n" );
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document.write( "Cheers,<BR>\n" );
document.write( "Stan H.<BR>\n" );
document.write( " </SPAN>\n" );
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