document.write( "<A HREF=/cgi-bin/jump-to-question.mpl?question=380911>Question 380911</A>: <I><SPAN STYLE=\"word-break: break-all;\"> The function f(x)=9x+1 is one-to-one. Find the inverse </SPAN>\n" );
document.write( "</I><HR><TABLE width=100%><TR><TD><B><A HREF=http://www.algebra.com/>Algebra.Com's</A> Answer #270333 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=270333\">put this solution on YOUR website!</A><BR><SPAN STYLE=\"word-break: break-all;\"> f(x) = 9x + 1\r<BR>\n" );
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document.write( "let y = f(x)\r<BR>\n" );
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document.write( "you get y = 9x + 1\r<BR>\n" );
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document.write( "let y = x and x = y\r<BR>\n" );
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document.write( "you get x = 9y + 1\r<BR>\n" );
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document.write( "solve for y to get y = (x-1)/9\r<BR>\n" );
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document.write( "that's your inverse function.\r<BR>\n" );
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document.write( "if it is a true inverse function, it will be a reflection of the original function about the line y = x.\r<BR>\n" );
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document.write( "to show that, then graph the functions y = x, y = 9x+1, y = (x-1)/9.\r<BR>\n" );
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document.write( "that graph is shown below:\r<BR>\n" );
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document.write( "you can pretty much eyeball it and see that the graph of y = (x-1)/9 is a reflection of y = 9x+1 about the line y = x.\r<BR>\n" );
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document.write( "a more exact interpretation is that f(x,y) in the normal equation should be equal to f(y,x) in the inverse equation.\r<BR>\n" );
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document.write( "how you find that out is as follows:\r<BR>\n" );
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document.write( "let x = 5 in the normal equation.\r<BR>\n" );
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document.write( "then you get y = 9x + 1 which becomes 46\r<BR>\n" );
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document.write( "in your normal equation, when x = 5, then y = 46\r<BR>\n" );
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document.write( "in your inverse equation, when x = 46, you should get y = 5.\r<BR>\n" );
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document.write( "the y in the normal equation becomes the x in the inverse equation.\r<BR>\n" );
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document.write( "the x in the normal equation becomes the y in the inverse equation.\r<BR>\n" );
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document.write( "when x = 46, y = (x-1)/9 becomes y = (46-1)/9 becomes y = 45/9 becomes 5.\r<BR>\n" );
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document.write( "f(x,y) = f(5,46) in your normal equation.\r<BR>\n" );
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document.write( "f(y,x) = f(46,5) in your inverse equation.\r<BR>\n" );
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document.write( "this proves they are inverse equations.\r<BR>\n" );
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document.write( "the inverse equation undoes what the normal equation does.\r<BR>\n" );
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document.write( "normal equation takes 5 and makes it 46.\r<BR>\n" );
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document.write( "inverse equation takes 46 and makes it 5.\r<BR>\n" );
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document.write( " </SPAN>\n" );
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