document.write( "<A HREF=/cgi-bin/jump-to-question.mpl?question=887162>Question 887162</A>: <I><SPAN STYLE=\"word-break: break-all;\"> This is a practice GRE question, I'm confused as I think (X^#)^# should equal X^2# or X^# times X^#.  For an answer they say the column A and B are equivalent.\r<BR>\n" );
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document.write( "For all numbers x, x^# = 24 - x.\r<BR>\n" );
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document.write( "Column A                                <BR>\n" );
document.write( "    ( x^#)^#\r<BR>\n" );
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document.write( "Column B<BR>\n" );
document.write( "    x<BR>\n" );
document.write( "                                    </SPAN>\n" );
document.write( "</I><HR><TABLE width=100%><TR><TD><B><A HREF=http://www.algebra.com/>Algebra.Com's</A> Answer #536417 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=536417\">put this solution on YOUR website!</A><BR><SPAN STYLE=\"word-break: break-all;\"> they are equivalent.\r<BR>\n" );
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document.write( "this is similar to:<BR>\n" );
document.write( "if f(x) = x^2 + 1, then f(x-3) = (x-3)^2 + 1<BR>\n" );
document.write( "you replace x with (x-3) in f(x) in order to get f(x-3) = (x-3)^2 + 1\r<BR>\n" );
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document.write( "this problem works the same way.\r<BR>\n" );
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document.write( "you have x^# = 24 - x\r<BR>\n" );
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document.write( "now they give you (x^#)^#<BR>\n" );
document.write( "because x^# = 24 - x, this becomes:<BR>\n" );
document.write( "(24-x)^#\r<BR>\n" );
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document.write( "now you have to replace x in the original function with (24 - x) and you will get:\r<BR>\n" );
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document.write( "(24-x)^# = 24 - (24-x) which becomes 24 - 24 + x which becomes x.\r<BR>\n" );
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document.write( "another way to look at it is to use another variable.\r<BR>\n" );
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document.write( "if x is any number, then y can also apply to the same logic because y can represent any number just as well as x can represent any number.\r<BR>\n" );
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document.write( "you get:\r<BR>\n" );
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document.write( "x^# = 24 - x<BR>\n" );
document.write( "you also get an equivalent function of:<BR>\n" );
document.write( "y^# = 24 - y\r<BR>\n" );
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document.write( "these functions are equivalent.<BR>\n" );
document.write( "you just replaced x with y.<BR>\n" );
document.write( "if x is 4 and y is 4, you'll get the same answer.\r<BR>\n" );
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document.write( "now start with (x^#)^#<BR>\n" );
document.write( "since x^# = 24-x, that becomes (24-x)^#<BR>\n" );
document.write( "now let y = (24-x) and you get:<BR>\n" );
document.write( "(24-x)^# = y^#<BR>\n" );
document.write( "now y^# = 24 - y, so your solution is 24 - y<BR>\n" );
document.write( "but y = 24 - x, so your solution becomes 24 - (24 - x) which becomes 24 - 24 + x which becomes x.\r<BR>\n" );
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document.write( "this is a real mind warper but the basics of the problem is functional notation and how its used.\r<BR>\n" );
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document.write( "f(x) = 5x + 7<BR>\n" );
document.write( "what is f(7)?<BR>\n" );
document.write( "you replace x with 7 and your equation becomes f(7) = 5*7 + 7 .....\r<BR>\n" );
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document.write( "f(x) = x^2<BR>\n" );
document.write( "what is f(x^2 + 3x - 2)?<BR>\n" );
document.write( "you replace x with x^2 + 3x - 2 to get:<BR>\n" );
document.write( "f(x^2 + 3x - 2) = (x^2 + 3x - 2)^2\r<BR>\n" );
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document.write( "it's the same concept even though you may not have seen it at first.\r<BR>\n" );
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document.write( " </SPAN>\n" );
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