document.write( "<A HREF=/cgi-bin/jump-to-question.mpl?question=165153>Question 165153</A>: <I><SPAN STYLE=\"word-break: break-all;\"> Given f(x) = x^2 + 1 and g(x) = x-2\r<BR>\n" );
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document.write( "a. Find (f-g)(-2)\r<BR>\n" );
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document.write( "b. Find f[g(5)]\r<BR>\n" );
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document.write( "Any help appreciated!  </SPAN>\n" );
document.write( "</I><HR><TABLE width=100%><TR><TD><B><A HREF=http://www.algebra.com/>Algebra.Com's</A> Answer #121741 by </B><A HREF=/tutors/aboutme.mpl?userid=gonzo><B>gonzo(654)</B></A><img src=\"/images/stars/stars-11.gif\" alt=\"\" >&nbsp;<A HREF=/tutors/aboutme.mpl?userid=gonzo><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=121741\">put this solution on YOUR website!</A><BR><SPAN STYLE=\"word-break: break-all;\"> problem a.<BR>\n" );
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document.write( "(f-g)(x) = f(x) - g(x)<BR>\n" );
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document.write( "(f-g)(-2) = f(-2) - g(-2)<BR>\n" );
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document.write( "f(x) = x^2 + 1<BR>\n" );
document.write( "f(-2) = (-2)^2 + 1<BR>\n" );
document.write( "f(-2) = 4+1<BR>\n" );
document.write( "f(-2) = 5<BR>\n" );
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document.write( "g(x) = x-2<BR>\n" );
document.write( "g(-2) = -2-2<BR>\n" );
document.write( "g(-2) = -4<BR>\n" );
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document.write( "f-g(-2) = f(-2) - g(-2) = 5 - (-4) = 5 + 4 = 9<BR>\n" );
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document.write( "answer for a is: <BR>\n" );
document.write( "f-g(-2) = 9<BR>\n" );
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document.write( "problem b.<BR>\n" );
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document.write( "g(x) = x-2<BR>\n" );
document.write( "g(5) = 5-2<BR>\n" );
document.write( "g(5) = 3<BR>\n" );
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document.write( "f(x) = x^2 + 1<BR>\n" );
document.write( "f(g(5)) = (g(5))^2 + 1<BR>\n" );
document.write( "since g(5) = 3, equation becomes:<BR>\n" );
document.write( "f(g(5)) = 3^2 + 1<BR>\n" );
document.write( "f(g(5)) = 9 + 1 = 10<BR>\n" );
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document.write( "answer for b is:<BR>\n" );
document.write( " f(g(5)) = 10<BR>\n" );
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document.write( "in general, you substitute whatever value is replacing x in the equation to get your answers.<BR>\n" );
document.write( "looking at problem b in this way, we would get a general solution as follows:<BR>\n" );
document.write( "f(x) = x^2 + 1<BR>\n" );
document.write( "g(x) = x-2<BR>\n" );
document.write( "substitute g(x) for x:<BR>\n" );
document.write( "f(g(x)) = (g(x))^2 + 1<BR>\n" );
document.write( "substitute the equation for g(x) on the right hand side.<BR>\n" );
document.write( "f(g(x)) = (x-2)^2 + 1<BR>\n" );
document.write( "remove parentheses:<BR>\n" );
document.write( "f(g(x)) = x^2 - 4*x + 4 + 1<BR>\n" );
document.write( "simplify:<BR>\n" );
document.write( "f(g(x)) = x^2 - 4*x + 5<BR>\n" );
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document.write( "substituting 5 for x:<BR>\n" );
document.write( "f(g(5)) = (5^2 - 4*5 + 5<BR>\n" );
document.write( "simplifying:<BR>\n" );
document.write( "f(g(5)) = 25 - 20 + 5<BR>\n" );
document.write( "f(g(5)) = 10<BR>\n" );
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document.write( "answer is the same as above where we first solved for g(5) which became 3, and then substituted that value in f(g(x)) which made it f(3)).<BR>\n" );
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document.write( "gonzo@gmx.us\r<BR>\n" );
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document.write( " </SPAN>\n" );
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