document.write( "<A HREF=/cgi-bin/jump-to-question.mpl?question=519189>Question 519189</A>: <I><SPAN STYLE=\"word-break: break-all;\">  Let f(x) = 2x - 4 and g(x) = 0.5x+2.<BR>\n" );
document.write( "Find 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 #345480 by </B><A HREF=/tutors/aboutme.mpl?userid=bucky><B>bucky(2189)</B></A><img src=\"/images/stars/stars-13.gif\" alt=\"\" >&nbsp;<A HREF=/tutors/aboutme.mpl?userid=bucky><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=345480\">put this solution on YOUR website!</A><BR><SPAN STYLE=\"word-break: break-all;\"> What does f(g(x)) mean? It means that you are to find f(x) when x is g(x). So all that this problem is asking you to do is to take the f(x) equation and replace any x in it with g(x).<BR>\n" );
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document.write( "So start with f(x) = 2x - 4<BR>\n" );
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document.write( "Then replace the x in f(x) with g(x), or to be more specific, on the left side of the f(x) equation, replace the x with g(x) and then on the right side of the f(x) equation replace any x with (0.5x + 2) which is the right side of the g(x)equation.<BR>\n" );
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document.write( "When you do that the left side gets written as f(g(x)) and the right side in which the x gets replaced with g(x) gets written as shown:<BR>\n" );
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document.write( "f(g(x)) = 2(0.5x + 2) - 4 <BR>\n" );
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document.write( "Then simplify the right side by doing the distributed multiplication (multiply 2 times each of the terms in the parentheses) and you have:<BR>\n" );
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document.write( "f(g(x)) = 2*0.5x + 2*2 - 4 = x + 4 - 4<BR>\n" );
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document.write( "Note that the +4 and the -4 cancel and you are left with just:<BR>\n" );
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document.write( "f(g(x)) = x<BR>\n" );
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document.write( "That's the answer you were to get.<BR>\n" );
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document.write( "Hopefully from this you have learned that f(g(x)) tells you to start with the right side of the f(x) equation and everywhere that you see an x you replace it with the right side of the equation for g(x) and then simplify it.<BR>\n" );
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