document.write( "<A HREF=/cgi-bin/jump-to-question.mpl?question=1200540>Question 1200540</A>: <I><SPAN STYLE=\"word-break: break-all;\"> f : x —> (2x + 7) / (x-2) for x ∈ R , x ≠ 2<BR>\n" );
document.write( "a) find an expression of f^-1 (x)<BR>\n" );
document.write( "b) State what your answer to part (a) tells you about the symmetry of the graph of y = f(x). </SPAN>\n" );
document.write( "</I><HR><TABLE width=100%><TR><TD><B><A HREF=http://www.algebra.com/>Algebra.Com's</A> Answer #834945 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=834945\">put this solution on YOUR website!</A><BR><SPAN STYLE=\"word-break: break-all;\"> i solved for the inverse equation and it turns out that the inverse equation is the same as the regular equation.<BR>\n" );
document.write( "here's how i did it.<BR>\n" );
document.write( "start with y = (2x+7) / (x-2)<BR>\n" );
document.write( "replace y with x and x with y to get:<BR>\n" );
document.write( "x = (2y+7) / (y-2)<BR>\n" );
document.write( "now you want to solve for y.<BR>\n" );
document.write( "multiply both sides of the equation by (y-2) to get:<BR>\n" );
document.write( "x * (y-2) = 2y+7<BR>\n" );
document.write( "simplify to get:<BR>\n" );
document.write( "yx - 2x = 2y + 7<BR>\n" );
document.write( "add 2x to both sides of the equation and subtract 2y from both sitdes of the equation to get:<BR>\n" );
document.write( "yx - 2y = 2x + 7<BR>\n" );
document.write( "factor out the y on the left side of the equation to get:<BR>\n" );
document.write( "y * (x-2) = 2x + 7<BR>\n" );
document.write( "divide both sides of the equation by (x-2) to get:<BR>\n" );
document.write( "y = (2x+7)/(x-2)<BR>\n" );
document.write( "the inverse equation is the same as the regular equation *****<BR>\n" );
document.write( "since the inverse equation is symmetric to the original equation about the line y = x, this says that the original equation is symmetric about the line y = x.<BR>\n" );
document.write( "a graph of the original equation should show this to be true.<BR>\n" );
document.write( "that's the only conclusion i can draw from this, since i can't think of anything else.<BR>\n" );
document.write( "here's the graph.<BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" src = \"http://theo.x10hosting.com/2023/030402.jpg\"><BR>\n" );
document.write( "i found a reference that seems to talk about this.<BR>\n" );
document.write( "it can be found at <a  rel=nofollow HREF= \"https://math.stackexchange.com/questions/541978/can-the-inverse-of-a-function-be-the-same-as-the-original-function\" target = \"_blank\">https://math.stackexchange.com/questions/541978/can-the-inverse-of-a-function-be-the-same-as-the-original-function</a><BR>\n" );
document.write( "the reference calls it an involution.<BR>\n" );
document.write( " </SPAN>\n" );
document.write( "</TD></TR></TABLE>\n" );