document.write( "<A HREF=/cgi-bin/jump-to-question.mpl?question=1204639>Question 1204639</A>: <I><SPAN STYLE=\"word-break: break-all;\"> use f(x)=-2x+4 and g(x)=x^2-3x to determine or simplify the following <BR>\n" );
document.write( "(a)f(3)<BR>\n" );
document.write( "(b)g(-2)<BR>\n" );
document.write( "(c)g(f(3))<BR>\n" );
document.write( "(d)f(g(x)) </SPAN>\n" );
document.write( "</I><HR><TABLE width=100%><TR><TD><B><A HREF=http://www.algebra.com/>Algebra.Com's</A> Answer #841028 by </B><A HREF=/tutors/aboutme.mpl?userid=math_tutor2020><B>math_tutor2020(3817)</B></A><img src=\"/images/stars/stars-13.gif\" alt=\"\" >&nbsp;<A HREF=/tutors/aboutme.mpl?userid=math_tutor2020><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=841028\">put this solution on YOUR website!</A><BR><SPAN STYLE=\"word-break: break-all;\"> <font color=black size=3><BR>\n" );
document.write( "Part (a)\r<BR>\n" );
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document.write( "f(x) = -2x+4<BR>\n" );
document.write( "f(3) = -2(3)+4<BR>\n" );
document.write( "f(3) = -6+4<BR>\n" );
document.write( "f(3) = <font color=red size=4>-2</font>\r<BR>\n" );
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document.write( "Part (b)\r<BR>\n" );
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document.write( "g(x) = x^2-3x<BR>\n" );
document.write( "g(-2) = (-2)^2-3(-2)<BR>\n" );
document.write( "g(-2) = 4+6<BR>\n" );
document.write( "g(-2) = <font color=red size=4>10</font>\r<BR>\n" );
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document.write( "Part (c)\r<BR>\n" );
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document.write( "g(f(3)) = g(-2) because f(3) = -2<BR>\n" );
document.write( "We replace f(3) with -2\r<BR>\n" );
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document.write( "Then refer to part (b) to find that g(-2) = <font color=red size=4>10</font> which must mean g(f(3)) = <font color=red size=4>10</font>\r<BR>\n" );
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document.write( "Here's another approach<BR>\n" );
document.write( "g(x) = x^2-3x<BR>\n" );
document.write( "g(x) = (x)^2-3(x)<BR>\n" );
document.write( "g(f(x)) = ( f(x) )^2-3( f(x) )<BR>\n" );
document.write( "g(f(x)) = (-2x+4)^2-3(-2x+4)<BR>\n" );
document.write( "g(f(x)) = (4x^2-16x+16)+(6x-12)<BR>\n" );
document.write( "g(f(x)) = 4x^2+(-16x+6x)+(16-12)<BR>\n" );
document.write( "g(f(x)) = 4x^2 - 10x + 4\r<BR>\n" );
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document.write( "Then,<BR>\n" );
document.write( "g(f(x)) = 4x^2 - 10x + 4<BR>\n" );
document.write( "g(f(3)) = 4(3)^2 - 10(3) + 4<BR>\n" );
document.write( "g(f(3)) = 4(9) - 10(3) + 4<BR>\n" );
document.write( "g(f(3)) = 36 - 30 + 4<BR>\n" );
document.write( "g(f(3)) = 6 + 4<BR>\n" );
document.write( "g(f(3)) = <font color=red size=4>10</font><BR>\n" );
document.write( "Your steps do not need to be as verbose as shown above.\r<BR>\n" );
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document.write( "Part (d)\r<BR>\n" );
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document.write( "f(x) = -2x + 4<BR>\n" );
document.write( "f(x) = -2( x ) + 4<BR>\n" );
document.write( "f(g(x)) = -2( g(x) ) + 4<BR>\n" );
document.write( "f(g(x)) = -2( x^2-3x ) + 4<BR>\n" );
document.write( "f(g(x)) = <font color=red size=4>-2x^2 + 6x + 4 </font>\r<BR>\n" );
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document.write( "Summary of the four answers<ol type=\"a\"><li>f(3) = <font color=red size=4>-2</font></li><li>g(-2) = <font color=red size=4>10</font></li><li>g(f(3)) = <font color=red size=4>10</font></li><li>f(g(x)) = <font color=red size=4>-2x^2 + 6x + 4 </font></li></ol>Each answer can be verified with GeoGebra.<BR>\n" );
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