document.write( "<A HREF=/cgi-bin/jump-to-question.mpl?question=1149579>Question 1149579</A>: <I><SPAN STYLE=\"word-break: break-all;\"> If f(2x+1)=6x+2 what is f(x)  </SPAN>\n" );
document.write( "</I><HR><TABLE width=100%><TR><TD><B><A HREF=http://www.algebra.com/>Algebra.Com's</A> Answer #770941 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=770941\">put this solution on YOUR website!</A><BR><SPAN STYLE=\"word-break: break-all;\"> <font face=\"times\" color=\"black\" size=\"3\"><BR>\n" );
document.write( "I'm assuming f(x) is some linear function. If so, then,<BR>\n" );
document.write( "f(x) = mx+b<BR>\n" );
document.write( "m = slope<BR>\n" );
document.write( "b = y intercept\r<BR>\n" );
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document.write( "Replace every x input with (2x+1) and simplify<BR>\n" );
document.write( "f(x) = mx+b<BR>\n" );
document.write( "f(2x+1) = m(2x+1) + b<BR>\n" );
document.write( "f(2x+1) = m*2x+m*1 + b<BR>\n" );
document.write( "f(2x+1) = 2mx+m+b\r<BR>\n" );
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document.write( "This is equal to 6x+2 since f(2x+1) = 6x+2 is given to us, so,<BR>\n" );
document.write( "2mx+m+b = 6x+2<BR>\n" );
document.write( "<font color=blue>2mx</font>+<font color=green>m+b</font> = <font color=blue>6x</font>+<font color=green>2</font>\r<BR>\n" );
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document.write( "Equating the two separate pieces has us see that<BR>\n" );
document.write( "<font color=blue>2mx</font> = <font color=blue>6x</font><BR>\n" );
document.write( "2m = 6<BR>\n" );
document.write( "m = 3\r<BR>\n" );
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document.write( "and also,<BR>\n" );
document.write( "<font color=green>m+b</font> = <font color=green>2</font><BR>\n" );
document.write( "3+b = 2 ... plug in m = 3<BR>\n" );
document.write( "b = -1\r<BR>\n" );
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document.write( "Therefore, m = 3 and b =  -1, meaning we can say<BR>\n" );
document.write( "f(x) = mx+b<BR>\n" );
document.write( "f(x) = 3x+(-1)<BR>\n" );
document.write( "<font color=red size=4>f(x) = 3x-1</font>\r<BR>\n" );
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document.write( "note that replacing every x with (2x+1) leads to...<BR>\n" );
document.write( "f(x) = 3x-1<BR>\n" );
document.write( "f(2x+1) = 3(2x+1)-1<BR>\n" );
document.write( "f(2x+1) = 3(2x)+3(1)-1<BR>\n" );
document.write( "f(2x+1) = 6x+3-1<BR>\n" );
document.write( "f(2x+1) = 6x+2<BR>\n" );
document.write( "which helps confirm our answer.<BR>\n" );
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