document.write( "<A HREF=/cgi-bin/jump-to-question.mpl?question=105814>Question 105814</A>: <I><SPAN STYLE=\"word-break: break-all;\"> I am not looking for any particular homework help, I would just like to get g(f(x)) explained to me. I don;t understand anything about it. </SPAN>\n" );
document.write( "</I><HR><TABLE width=100%><TR><TD><B><A HREF=http://www.algebra.com/>Algebra.Com's</A> Answer #77010 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=77010\">put this solution on YOUR website!</A><BR><SPAN STYLE=\"word-break: break-all;\"> If you are given two functions ... one of them f(x) and the other g(x) all that it means if<BR>\n" );
document.write( "you are asked to find g(f(x)) is to go to g(x) and for every x you find in it, substitute<BR>\n" );
document.write( "f(x).<BR>\n" );
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document.write( "As an example. Suppose you are given:<BR>\n" );
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document.write( "f(x) = 2x - 1 and<BR>\n" );
document.write( "g(x) = x^2 - 2x + 3<BR>\n" );
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document.write( "To find g(f(x)) means start with g(x) and in place of the x in the terms it contains,<BR>\n" );
document.write( "substitute the right side of the equation for f(x).<BR>\n" );
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document.write( "Start with:<BR>\n" );
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document.write( "g(x) = x^2 - 2x + 3<BR>\n" );
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document.write( "In place of each of the x's in g(x) substitute 2x - 1 to get g(f(x))<BR>\n" );
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document.write( "g(f(x)) = (2x-1)^2 - 2(2x - 1) + 3<BR>\n" );
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document.write( "Look carefully at this ... see how the x's in g(x) have been replaced by 2x -1 which is f(x).<BR>\n" );
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document.write( "Now all you have to do is the math. Square out (2x - 1) to get 4x^2 - 4x + 1 and multiply<BR>\n" );
document.write( "-2 times (2x - 1) to get -4x + 2<BR>\n" );
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document.write( "Substitute these multiplications to get:<BR>\n" );
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document.write( "g(f(x)) = 4x^2 - 4x + 1 - 4x + 2 + 3<BR>\n" );
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document.write( "On the right side combine the -4x and the -4x to get -8x and combine the +1 with the +2 and<BR>\n" );
document.write( "the +3 to get +6. Insert these results and the equation for g(f(x)) becomes:<BR>\n" );
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document.write( "g(f(x)) = 4x^2 - 8x + 6<BR>\n" );
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document.write( "Hopefully this example makes sense to you and you can see how g(f(x)) is found when you <BR>\n" );
document.write( "are given both g(x) and f(x).<BR>\n" );
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