document.write( "<A HREF=/cgi-bin/jump-to-question.mpl?question=74102>Question 74102</A>: <I><SPAN STYLE=\"word-break: break-all;\"> f(a+b) = f(a)+ f(b) for all positive numbers a and b<BR>\n" );
document.write( "a) f(x) = x squared<BR>\n" );
document.write( "b) f(x) = x+1<BR>\n" );
document.write( "c) f(x) = square root x<BR>\n" );
document.write( "d) f(x) = 2/x<BR>\n" );
document.write( "e) f(x) = -3x\r<BR>\n" );
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document.write( "Thanks,<BR>\n" );
document.write( "Casey </SPAN>\n" );
document.write( "</I><HR><TABLE width=100%><TR><TD><B><A HREF=http://www.algebra.com/>Algebra.Com's</A> Answer #53164 by </B><A HREF=/tutors/aboutme.mpl?userid=jim_thompson5910><B>jim_thompson5910(35256)</B></A><img src=\"/images/stars/stars-13.gif\" alt=\"\" >&nbsp;<A HREF=/tutors/aboutme.mpl?userid=jim_thompson5910><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=53164\">put this solution on YOUR website!</A><BR><SPAN STYLE=\"word-break: break-all;\"> If we let a=2 and b=3 (arbitrary numbers) and we plug them into each possible equation, we can eliminate the wrong answers.\r<BR>\n" );
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document.write( "a)Lets start with our first possible answer.<BR>\n" );
document.write( "f(a+b) = f(a)+ f(b) Plug in a=2,b=3<BR>\n" );
document.write( "f(2+3)=f(2)+f(3)<BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=%282%2B3%29%5E2=2%5E2%2B3%5E2 ALIGN=MIDDLE  ALT=\"%282%2B3%29%5E2=2%5E2%2B3%5E2\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=25=4%2B9 ALIGN=MIDDLE  ALT=\"25=4%2B9\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=25=9 ALIGN=MIDDLE  ALT=\"25=9\"   DISABLED_style= \"max-width:90%; height:auto;\" >Which is obviously not equal, so that eliminates a) continue with the rest by plugging in a+b in for x on the left and a and b separately for x on the right.\r<BR>\n" );
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document.write( "b)<BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=%282%2B3%29%2B1=%282%2B1%29%2B%283%2B1%29 ALIGN=MIDDLE  ALT=\"%282%2B3%29%2B1=%282%2B1%29%2B%283%2B1%29\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=6=7 ALIGN=MIDDLE  ALT=\"6=7\"   DISABLED_style= \"max-width:90%; height:auto;\" >Which is not equal, that eliminates b)\r<BR>\n" );
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document.write( "c)<BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=sqrt%282%2B3%29=sqrt%282%29%2Bsqrt%283%29 ALIGN=MIDDLE  ALT=\"sqrt%282%2B3%29=sqrt%282%29%2Bsqrt%283%29\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=sqrt%285%29=1.414%2B1.732 ALIGN=MIDDLE  ALT=\"sqrt%285%29=1.414%2B1.732\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=2.236=3.146 ALIGN=MIDDLE  ALT=\"2.236=3.146\"   DISABLED_style= \"max-width:90%; height:auto;\" >Which is not equal, so that eliminates c)\r<BR>\n" );
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document.write( "d)<BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=2%2F%282%2B3%29=2%2F2%2B2%2F3 ALIGN=MIDDLE  ALT=\"2%2F%282%2B3%29=2%2F2%2B2%2F3\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=2%2F5=1%2B2%2F3 ALIGN=MIDDLE  ALT=\"2%2F5=1%2B2%2F3\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=2%2F5=5%2F3 ALIGN=MIDDLE  ALT=\"2%2F5=5%2F3\"   DISABLED_style= \"max-width:90%; height:auto;\" >Not equal, that eliminates d). There's only one left, lets verify if this is our answer.\r<BR>\n" );
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document.write( "e)<BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=-3%282%2B3%29=-3%282%29%2B%28-3%283%29%29 ALIGN=MIDDLE  ALT=\"-3%282%2B3%29=-3%282%29%2B%28-3%283%29%29\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=-3%285%29=-6-9 ALIGN=MIDDLE  ALT=\"-3%285%29=-6-9\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=-15=-15 ALIGN=MIDDLE  ALT=\"-15=-15\"   DISABLED_style= \"max-width:90%; height:auto;\" >Which works. Notice how the two sides are simply the right side has distributed the -3 where the left side factored the -3 </SPAN>\n" );
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