document.write( "<A HREF=/cgi-bin/jump-to-question.mpl?question=163839>Question 163839</A>: <I><SPAN STYLE=\"word-break: break-all;\"> supposed f(x)=-4x+3 and g(x)=1/x+2.  evaluated f(g(x)) and g(f(x)) for x.  Note any restrictions. show your work.<BR>\n" );
document.write( "THANK YOU! </SPAN>\n" );
document.write( "</I><HR><TABLE width=100%><TR><TD><B><A HREF=http://www.algebra.com/>Algebra.Com's</A> Answer #120707 by </B><A HREF=/tutors/aboutme.mpl?userid=midwood_trail><B>midwood_trail(310)</B></A><img src=\"/images/stars/stars-10.gif\" alt=\"\" >&nbsp;<A HREF=/tutors/aboutme.mpl?userid=midwood_trail><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=120707\">put this solution on YOUR website!</A><BR><SPAN STYLE=\"word-break: break-all;\"> Supposed f(x)=-4x+3 and g(x)=1/x+2.  Evaluated f(g(x)) and g(f(x)) for x.  Note any restrictions. Show your work.\r<BR>\n" );
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document.write( "f(g(x)) means to plug the value of g(x) in the function f(x) and simplify.\r<BR>\n" );
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document.write( "f(1/(x+2))....Everywhere you see an x for f(x), replace it with the value <BR>\n" );
document.write( "of g(x), which is the fraction 1/(x+2).\r<BR>\n" );
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document.write( "This is what it looks like:\r<BR>\n" );
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document.write( "f(1/(x+2)) = -4(1/(x+2)) + 3\r<BR>\n" );
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document.write( "f(1/(x+2)) = -4/(x + 2) + 3\r<BR>\n" );
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document.write( "We can write 3 as 3/1 to make our fraction work easier.\r<BR>\n" );
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document.write( "We add -4/(x + 2) + 3/1 and get (3x + 2)/(x + 2) for f(g(x)).\r<BR>\n" );
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document.write( "The restriction is the domain.  In other words, the restriction will be the value(s) we can safely replace x with in the final answer without producing division by zero.\r<BR>\n" );
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document.write( "For the fraction, (3x + 2)/(x + 2), x can be all real numbers <BR>\n" );
document.write( "EXCEPT x CANNOT = -2. If you replace x with -2 in the above fraction, you will create division by zero, which does not exist or is UNDEFINED.\r<BR>\n" );
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document.write( "So, f(g(x)) = (3x + 2)/(x + 2) with restriction x = all real numbers EXCEPT that x cannot = -2.\r<BR>\n" );
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document.write( "Is this clear?\r<BR>\n" );
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document.write( "To find or evaluate g(f(x)), we replace every x that you see for<BR>\n" );
document.write( "g(x) with -4x + 3 and simplify.\r<BR>\n" );
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document.write( "g(f(x)) = g(-4x + 3)\r<BR>\n" );
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document.write( "Then:\r<BR>\n" );
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document.write( "g(-4x + 3) = 1/(-4x + 3) + 2\r<BR>\n" );
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document.write( "We simplify the denominator in the fraction 1/(-4x + 3) + 2 and we get:\r<BR>\n" );
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document.write( "1/(-4x + 5)\r<BR>\n" );
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document.write( "So, g(f(x)) = 1/(-4x + 5) with restriction or domain x = all real numbers \r<BR>\n" );
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document.write( "EXCEPT x cannot = 5/4 because the fraction 5/4 will <BR>\n" );
document.write( "create division by zero in the fraction 1/(-4x + 5), which does not exist or is UNDEFINED.\r<BR>\n" );
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document.write( "Did you follow?\r<BR>\n" );
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document.write( " </SPAN>\n" );
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