document.write( "<A HREF=/cgi-bin/jump-to-question.mpl?question=279635>Question 279635</A>: <I><SPAN STYLE=\"word-break: break-all;\"> how do you get the inverse of y=2/x </SPAN>\n" );
document.write( "</I><HR><TABLE width=100%><TR><TD><B><A HREF=http://www.algebra.com/>Algebra.Com's</A> Answer #203252 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=203252\">put this solution on YOUR website!</A><BR><SPAN STYLE=\"word-break: break-all;\"> equation is y = 2/x\r<BR>\n" );
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document.write( "solve for x.\r<BR>\n" );
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document.write( "multiply both sides of the equation by x to get:\r<BR>\n" );
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document.write( "xy = 2\r<BR>\n" );
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document.write( "divide both sides of the equation by y to get:\r<BR>\n" );
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document.write( "x = 2/y\r<BR>\n" );
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document.write( "replace x with y and y with x to get:\r<BR>\n" );
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document.write( "y = 2/x\r<BR>\n" );
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document.write( "this equation is the inverse of itself.\r<BR>\n" );
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document.write( "your equation is y = 2/x\r<BR>\n" );
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document.write( "the inverse equation is y = 2/x\r<BR>\n" );
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document.write( "A graph of your equation and the line y = x looks like this:\r<BR>\n" );
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document.write( "based on the graph, your equation looks like it is symmetric with respect to the line y = x\r<BR>\n" );
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document.write( "let's set y equal to f(x) in the original equation of y = 2/x.   \r<BR>\n" );
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document.write( "y = 2/x becomes f(x) = 2/x.\r<BR>\n" );
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document.write( "let's set y equal to g(x) in the inverse equation of y = 2/x.   \r<BR>\n" );
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document.write( "y = 2/x becomes g(x) = 2/x.\r<BR>\n" );
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document.write( "now we can distinguish between them.\r<BR>\n" );
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document.write( "f(x) = 2/x is the original equation.<BR>\n" );
document.write( "g(x) = 2/x is the inverse equation.\r<BR>\n" );
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document.write( "the fact that they represent the same equation is an anomaly of the inverse function rules but the rules still hold.\r<BR>\n" );
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document.write( "if they are truly inverse equations of each other, then for every x in f(x), we should have g(f(x)) = x.\r<BR>\n" );
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document.write( "to see if that's true, let's do the following:\r<BR>\n" );
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document.write( "let x = 6.\r<BR>\n" );
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document.write( "f(x) = 2/x = 2/6 = 1/3\r<BR>\n" );
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document.write( "since f(x) = 1/3, then g(f(x)) = g(1/3).\r<BR>\n" );
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document.write( "since g(x) = 2/x, then g(1/3) = 2 / (1/3) which equals 6.\r<BR>\n" );
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document.write( "we simply replace x with 1/3 in the equation.\r<BR>\n" );
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document.write( "there we have it.\r<BR>\n" );
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document.write( "g(f(x)) = x\r<BR>\n" );
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document.write( "x = 6<BR>\n" );
document.write( "f(x) = 1/3<BR>\n" );
document.write( "g(1/3) = 6\r<BR>\n" );
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document.write( "the test for inverse function is passed and this function is the inverse function of itself.\r<BR>\n" );
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