document.write( "<A HREF=/cgi-bin/jump-to-question.mpl?question=682489>Question 682489</A>: <I><SPAN STYLE=\"word-break: break-all;\"> Find a formula for f^-1(x). Give the domain of f^-1, including any restrictions \"inherited\" from f. <BR>\n" );
document.write( "f(x)= 2x-3/x+1\r<BR>\n" );
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document.write( "I have tried replacing the x as a y: <BR>\n" );
document.write( "x = 2y-3/y+1<BR>\n" );
document.write( "y+1(x) = 2y-3<BR>\n" );
document.write( "y = 2y-3/1x\r<BR>\n" );
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document.write( "That's as far as I got, and I don't know how to determine if there are restrictions on f(x) or f^-1 (x). </SPAN>\n" );
document.write( "</I><HR><TABLE width=100%><TR><TD><B><A HREF=http://www.algebra.com/>Algebra.Com's</A> Answer #423237 by </B><A HREF=/tutors/aboutme.mpl?userid=ReadingBoosters><B>ReadingBoosters(3246)</B></A><img src=\"/images/stars/stars-13.gif\" alt=\"\" >&nbsp;<A HREF=/tutors/aboutme.mpl?userid=ReadingBoosters><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/images/nopicture.jpg><BR>You can <A HREF=\"/cgi-bin/embed-solution.mpl?show=1&solution=423237\">put this solution on YOUR website!</A><BR><SPAN STYLE=\"word-break: break-all;\"> Inverse function is NOT determined by swapping x and y then solving y, <BR>\n" );
document.write( "it IS determined by solving for x and then swapping the x and y variables.<BR>\n" );
document.write( "y = <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=%282x-3%29%2F%28x%2B1%29 ALIGN=MIDDLE  ALT=\"%282x-3%29%2F%28x%2B1%29\"   DISABLED_style= \"max-width:90%; height:auto;\" > ==> multiply both sides by (x+1)<BR>\n" );
document.write( "y(x+1) = (2x-3) ==> distribute the y<BR>\n" );
document.write( "xy+y = 2x-3 ==> group x variables on the left<BR>\n" );
document.write( "xy + 2x = -3 - y ==> factor out the x variable<BR>\n" );
document.write( "x(y+2) = -3 - y ==> divide both sides by (y+2) to isolate x<BR>\n" );
document.write( "x = (-3-y)/(y+2) ==> swap x and y variables<BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=f%5E-1%28x%29+=+%28-3-x%29%2F%28x%2B2%29 ALIGN=MIDDLE  ALT=\"f%5E-1%28x%29+=+%28-3-x%29%2F%28x%2B2%29\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "...<BR>\n" );
document.write( "restriction in f(x) is <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=x%2B1%3C%3E0 ALIGN=MIDDLE  ALT=\"x%2B1%3C%3E0\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=x%3C%3E-1 ALIGN=MIDDLE  ALT=\"x%3C%3E-1\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "restriction in <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=f%5E-1 ALIGN=MIDDLE  ALT=\"f%5E-1\"   DISABLED_style= \"max-width:90%; height:auto;\" > is <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=x%2B2%3C%3E0 ALIGN=MIDDLE  ALT=\"x%2B2%3C%3E0\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=x%3C%3E-2 ALIGN=MIDDLE  ALT=\"x%3C%3E-2\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "...<BR>\n" );
document.write( "domain is all real numbers except -1 and -2<BR>\n" );
document.write( ".....................<BR>\n" );
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document.write( " </SPAN>\n" );
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