document.write( "<A HREF=/cgi-bin/jump-to-question.mpl?question=1004226>Question 1004226</A>: <I><SPAN STYLE=\"word-break: break-all;\"> If (f*g)(x)= x^2-6x+8 and g(x)= x-3 , which expression could represent f(x)?\r<BR>\n" );
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document.write( " a. x – 4 <BR>\n" );
document.write( " b. x – 1 <BR>\n" );
document.write( " c. x^2 - 1<BR>\n" );
document.write( " d. x^2 - 6x +5\r<BR>\n" );
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document.write( "When they don't give you a value to input as x, do you just multiply the two equations together?  </SPAN>\n" );
document.write( "</I><HR><TABLE width=100%><TR><TD><B><A HREF=http://www.algebra.com/>Algebra.Com's</A> Answer #620758 by </B><A HREF=/tutors/aboutme.mpl?userid=rothauserc><B>rothauserc(4718)</B></A><img src=\"/images/stars/stars-13.gif\" alt=\"\" >&nbsp;<A HREF=/tutors/aboutme.mpl?userid=rothauserc><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=rothauserc><BR>You can <A HREF=\"/cgi-bin/embed-solution.mpl?show=1&solution=620758\">put this solution on YOUR website!</A><BR><SPAN STYLE=\"word-break: break-all;\"> The problem would be written as f * g or f(x) * g(x) if you multiplied to find the answer.<BR>\n" );
document.write( "However, the problem is written (f*g)(x) which is the composite function.  In order to do this, you apply g first and then f.<BR>\n" );
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document.write( "We are given the composite function,<BR>\n" );
document.write( "(f*g)(x) = x^2 -6x + 8 and g(x) = x-3 and<BR>\n" );
document.write( "4 possibilities for f(x),however, we know there has to be an x^2 term in f(x) since there is an x^2 term in the composite - therefore we need only check c and d, let's check them by substituting x-3 for x in each possibility<BR>\n" );
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document.write( "c) (x-3)^2 - 1 = x^2 -6x +9 - 1 = x^2 -6x +8<BR>\n" );
document.write( "therefore c is the answer, but let's check d also<BR>\n" );
document.write( "d) (x-3)^2 -6(x-3) + 5 = x^2 -6x +9 -18x +18 +5 = x^2 -24x +32<BR>\n" );
document.write( "d does not give us the composite function<BR>\n" );
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document.write( "c is the answer\r<BR>\n" );
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