document.write( "<A HREF=/cgi-bin/jump-to-question.mpl?question=1134048>Question 1134048</A>: <I><SPAN STYLE=\"word-break: break-all;\"> 	(8 pts) Let f(x) = (x +  7)/(x- 5)^2 \r<BR>\n" );
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document.write( "	Calculate f(-3). Show the answer in exact form, simplified\r<BR>\n" );
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document.write( "	State the domain of the function.\r<BR>\n" );
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document.write( "	Determine f(a+3) and simplify as much as possible. Show work.\r<BR>\n" );
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document.write( "</I><HR><TABLE width=100%><TR><TD><B><A HREF=http://www.algebra.com/>Algebra.Com's</A> Answer #751332 by </B><A HREF=/tutors/aboutme.mpl?userid=Theo><B>Theo(13342)</B></A><img src=\"/images/stars/stars-13.gif\" alt=\"\" >&nbsp;<A HREF=/tutors/aboutme.mpl?userid=Theo><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/cgi-bin/show-face.mpl?user=Theo><BR>You can <A HREF=\"/cgi-bin/embed-solution.mpl?show=1&solution=751332\">put this solution on YOUR website!</A><BR><SPAN STYLE=\"word-break: break-all;\"> f(x) = (x + 7) * (x - 5)^2\r<BR>\n" );
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document.write( "f(-3) = (-3 + 7) * (-3 - 5)^2<BR>\n" );
document.write( "simplify to get f(-3) = 4 * (-8)^2<BR>\n" );
document.write( "simplify further to get f(-3) = 4 * 64<BR>\n" );
document.write( "simplify further to get f(-3) = 256\r<BR>\n" );
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document.write( "that's your solution to the first part.\r<BR>\n" );
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document.write( "for the second part, start again with f(x) = (x + 7) * (x - 5)^2\r<BR>\n" );
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document.write( "replace x with a + 3 to get:\r<BR>\n" );
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document.write( "f(a + 3) = (a + 3 + 7) * (a + 3 - 5)^2\r<BR>\n" );
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document.write( "combine like terms to get:\r<BR>\n" );
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document.write( "f(a + 3) = (a + 10) * (a - 2)^2\r<BR>\n" );
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document.write( "since (a - 2)^2 is equal to a^2 - 4a + 4, the equation becomes:\r<BR>\n" );
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document.write( "f(a + 3) = (a + 10) * (a^2 - 4a + 4)\r<BR>\n" );
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document.write( "simplify to get:\r<BR>\n" );
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document.write( "f(a + 3) = a * (a^2 - 4a + 4) + 10 * (a^2 - 4a + 4)\r<BR>\n" );
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document.write( "simplify further to get:\r<BR>\n" );
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document.write( "f(a + 3) = a^3 - 4a^2 + 4a + 10a^2 - 40a + 40\r<BR>\n" );
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document.write( "combine like terms to get:\r<BR>\n" );
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document.write( "f(a + 3) = a^3 + 6a^2 - 36a + 40\r<BR>\n" );
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document.write( "that's your final equation for f(a + 3).\r<BR>\n" );
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document.write( "to see if the final equation is equivalent to the starting equation, select a random value for a and then evaluate the starting equation and the final equation to see if they provide the same answer.\r<BR>\n" );
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document.write( "your starting equation was f(a + 3) = (a + 3 + 7) * (a + 3 - 5)^2\r<BR>\n" );
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document.write( "your final equation was f(a + 3) = a^3 + 6a^2 - 36a + 40\r<BR>\n" );
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document.write( "let a = 5.\r<BR>\n" );
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document.write( "your starting equation becomes f(5 + 3) = (5 + 3 + 7) * (5 + 3 - 5)^2<BR>\n" );
document.write( "this becomes f(8) = 15 * 9 = 135\r<BR>\n" );
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document.write( "your final equation becomes f(5 + 3) = 5^3 + 6*5^2 - 36*5 + 40<BR>\n" );
document.write( "this becomes f(8) = 125 + 150 - 180 + 40<BR>\n" );
document.write( "this becomes f(8) = 135\r<BR>\n" );
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document.write( "starting equation and final equation provide the same answer, so the simplification must have been good.\r<BR>\n" );
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