document.write( "<A HREF=/cgi-bin/jump-to-question.mpl?question=250480>Question 250480</A>: <I><SPAN STYLE=\"word-break: break-all;\"> whAT IS THE INVERSE OF THE ONE TO ONE FUNCTION  f(X)= 6X-7 DIVIDED BY 5 </SPAN>\n" );
document.write( "</I><HR><TABLE width=100%><TR><TD><B><A HREF=http://www.algebra.com/>Algebra.Com's</A> Answer #182355 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=182355\">put this solution on YOUR website!</A><BR><SPAN STYLE=\"word-break: break-all;\"> f(x) = (6x-7)/5\r<BR>\n" );
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document.write( "In this equation, solve for x.\r<BR>\n" );
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document.write( "multiply both sides of the equation by 5 to get:\r<BR>\n" );
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document.write( "5 * f(x) = 6x - 7\r<BR>\n" );
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document.write( "add 7 to both sides of this equation to get:\r<BR>\n" );
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document.write( "5 * f(x) + 7 = 6x\r<BR>\n" );
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document.write( "divide both sides of this equation by 6 to get:\r<BR>\n" );
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document.write( "(5 * f(x) + 7) / 6 = x\r<BR>\n" );
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document.write( "replace x with f(x) and replace f(x) with x (interchange them).\r<BR>\n" );
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document.write( "equation becomes:\r<BR>\n" );
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document.write( "(5 * x + 7) / 6 = f(x)\r<BR>\n" );
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document.write( "that's the same as:\r<BR>\n" );
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document.write( "f(x) = (5 * x + 7) / 6\r<BR>\n" );
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document.write( "that's your inverse function.\r<BR>\n" );
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document.write( "graph both equation to see that they are symmetric about the line y = x.\r<BR>\n" );
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document.write( "the graph looks like the lines are symmetric and reflections of each other about the line y = x so it appears that these are inverse functions.\r<BR>\n" );
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document.write( "test a point to see if they are symmetric about the line y = x.\r<BR>\n" );
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document.write( "If so, then the point (x,y) in one equation should be equal to the point (y,x) in the other equation.\r<BR>\n" );
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document.write( "try x = -15 the first equation.\r<BR>\n" );
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document.write( "at x = -15, y = (6x-7)/5 = -18\r<BR>\n" );
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document.write( "(x,y) = (-15,-18) in the first equation.\r<BR>\n" );
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document.write( "let x = -18 in the second equation.  This is the value of y in the first equation.\r<BR>\n" );
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document.write( "at x = -18, y (5 * -18 / 6) = -15.  This is the value of x in the first equation.\r<BR>\n" );
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document.write( "(y,x) = (-18,-15) in the second equation.\r<BR>\n" );
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document.write( "the point (x,y) = (-15,-18) in the first equation is equal to the point (y,x) = (-18,-15) in the second equation so the lines are symmetric about the line y = x.\r<BR>\n" );
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document.write( "in the equations above, if you let y = f(x), then where I have used y you can substitute f(x), and where I have used f(x) you can substitute y, as necessary, in order to put the equation in the form that you need.\r<BR>\n" );
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document.write( "They both mean the same thing.\r<BR>\n" );
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