document.write( "<A HREF=/cgi-bin/jump-to-question.mpl?question=1104188>Question 1104188</A>: <I><SPAN STYLE=\"word-break: break-all;\"> Please help me with this question: If f(x) = x^2-x-1 and f[g(x)]=4x^2 + 10x + 5, find g(x).<BR>\n" );
document.write( "Any help will be greatly appreciated!  </SPAN>\n" );
document.write( "</I><HR><TABLE width=100%><TR><TD><B><A HREF=http://www.algebra.com/>Algebra.Com's</A> Answer #718920 by </B><A HREF=/tutors/aboutme.mpl?userid=math_helper><B>math_helper(2461)</B></A><img src=\"/images/stars/stars-13.gif\" alt=\"\" >&nbsp;<A HREF=/tutors/aboutme.mpl?userid=math_helper><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/cgi-bin/show-face.mpl?user=math_helper><BR>You can <A HREF=\"/cgi-bin/embed-solution.mpl?show=1&solution=718920\">put this solution on YOUR website!</A><BR><SPAN STYLE=\"word-break: break-all;\"> I found it by trial and error, using hints from  <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=+f%28g%28x%29%29+=+4x%5E2+%2B+10x+%2B+5+ ALIGN=MIDDLE  ALT=\"+f%28g%28x%29%29+=+4x%5E2+%2B+10x+%2B+5+\"   DISABLED_style= \"max-width:90%; height:auto;\" >\r<BR>\n" );
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document.write( "I assumed  <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=+g%28x%29+=+ax+%2B+b+ ALIGN=MIDDLE  ALT=\"+g%28x%29+=+ax+%2B+b+\"   DISABLED_style= \"max-width:90%; height:auto;\" >    <BR>\n" );
document.write( "where a=2 because we need to end up with <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=4x%5E2 ALIGN=MIDDLE  ALT=\"4x%5E2\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "and   2ab - a = 10  —>  a(2b-1) = 10  (EDIT: because a=2, this implies b=3, missed that earlier)<BR>\n" );
document.write( "Another hint/constraint is that  <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=+b%5E2+-+b+-+1+=+5+ ALIGN=MIDDLE  ALT=\"+b%5E2+-+b+-+1+=+5+\"   DISABLED_style= \"max-width:90%; height:auto;\" > \r<BR>\n" );
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document.write( "I found a=2 and b=3 works.   <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=+g%28x%29+=+2x+%2B+3+ ALIGN=MIDDLE  ALT=\"+g%28x%29+=+2x+%2B+3+\"   DISABLED_style= \"max-width:90%; height:auto;\" > <BR>\n" );
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document.write( "—<BR>\n" );
document.write( "Of course, this worked out because I guessed the proper form for g(x).  <BR>\n" );
document.write( "Maybe another tutor may have a more structured method.   I'm often amazed at the talent base here.<BR>\n" );
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