document.write( "<A HREF=/cgi-bin/jump-to-question.mpl?question=944944>Question 944944</A>: <I><SPAN STYLE=\"word-break: break-all;\"> given f(x)=f(x+1)+3 and f(2)=5, what is the value of f(8)  </SPAN>\n" );
document.write( "</I><HR><TABLE width=100%><TR><TD><B><A HREF=http://www.algebra.com/>Algebra.Com's</A> Answer #576202 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=576202\">put this solution on YOUR website!</A><BR><SPAN STYLE=\"word-break: break-all;\"> given f(x)=f(x+1)+3 and f(2)=5, what is the value of f(8) <BR>\n" );
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document.write( "First isolate f(x+1)\r<BR>\n" );
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document.write( "f(x)=f(x+1)+3<BR>\n" );
document.write( "f(x)-3=f(x+1)<BR>\n" );
document.write( "f(x+1) = f(x) - 3<BR>\n" );
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document.write( "Because f(x+1) = f(x) - 3, we need to build our way up to f(8) by finding f(7), f(6), etc all the way down until f(3)<BR>\n" );
document.write( "So let's find f(3)\r<BR>\n" );
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document.write( "f(x+1) = f(x) - 3<BR>\n" );
document.write( "f(2+1) = f(2) - 3<BR>\n" );
document.write( "f(3) = f(2) - 3<BR>\n" );
document.write( "f(3) = 5 - 3<BR>\n" );
document.write( "f(3) = 2<BR>\n" );
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document.write( "and then use this to find f(4)\r<BR>\n" );
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document.write( "f(x+1) = f(x) - 3<BR>\n" );
document.write( "f(3+1) = f(3) - 3<BR>\n" );
document.write( "f(4) = f(3) - 3<BR>\n" );
document.write( "f(4) = 2 - 3<BR>\n" );
document.write( "f(4) = -1<BR>\n" );
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document.write( "we do the same for f(5)\r<BR>\n" );
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document.write( "f(x+1) = f(x) - 3<BR>\n" );
document.write( "f(4+1) = f(4) - 3<BR>\n" );
document.write( "f(5) = f(4) - 3<BR>\n" );
document.write( "f(5) = -1 - 3<BR>\n" );
document.write( "f(5) = -4<BR>\n" );
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document.write( "and so on...until we reach f(8)\r<BR>\n" );
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document.write( "f(x+1) = f(x) - 3<BR>\n" );
document.write( "f(5+1) = f(5) - 3<BR>\n" );
document.write( "f(6) = f(5) - 3<BR>\n" );
document.write( "f(6) = -4 - 3<BR>\n" );
document.write( "f(6) = -7<BR>\n" );
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document.write( "f(x+1) = f(x) - 3<BR>\n" );
document.write( "f(6+1) = f(6) - 3<BR>\n" );
document.write( "f(7) = f(6) - 3<BR>\n" );
document.write( "f(7) = -7 - 3<BR>\n" );
document.write( "f(7) = -10<BR>\n" );
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document.write( "f(x+1) = f(x) - 3<BR>\n" );
document.write( "f(7+1) = f(7) - 3<BR>\n" );
document.write( "f(8) = f(7) - 3<BR>\n" );
document.write( "f(8) = -10 - 3<BR>\n" );
document.write( "f(8) = -13<BR>\n" );
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document.write( "So in the end, we find that f(8) = <font color=\"red\">-13</font> </SPAN>\n" );
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