document.write( "<A HREF=/cgi-bin/jump-to-question.mpl?question=266599>Question 266599</A>: <I><SPAN STYLE=\"word-break: break-all;\"> show that f(x)=(x-2)/(x+3) is invertible by finding its inverse.<BR>\n" );
document.write( "(a) what is the domain of f(x)? the range of f-1(x)?<BR>\n" );
document.write( "(b) what is the domain of f-(x)? the range of 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 #195872 by </B><A HREF=/tutors/aboutme.mpl?userid=drk><B>drk(1908)</B></A><img src=\"/images/stars/stars-12.gif\" alt=\"\" >&nbsp;<A HREF=/tutors/aboutme.mpl?userid=drk><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=195872\">put this solution on YOUR website!</A><BR><SPAN STYLE=\"word-break: break-all;\"> Here is the original equation<BR>\n" );
document.write( "(i) <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=f%28x%29=%28x-2%29%2F%28x%2B3%29 ALIGN=MIDDLE  ALT=\"f%28x%29=%28x-2%29%2F%28x%2B3%29\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "to find the inverse switch the x and y parts.<BR>\n" );
document.write( "(ii) <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=x+=+%28y-2%29%2F%28y%2B3%29 ALIGN=MIDDLE  ALT=\"x+=+%28y-2%29%2F%28y%2B3%29\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "cross multiply to get<BR>\n" );
document.write( "(iii) <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=xy+%2B+3x+=+y-2 ALIGN=MIDDLE  ALT=\"xy+%2B+3x+=+y-2\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "add 2 and then subtract xy to get<BR>\n" );
document.write( "(iv) <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=+3x%2B2+=+y+-+xy ALIGN=MIDDLE  ALT=\"+3x%2B2+=+y+-+xy\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "factor out the y to get<BR>\n" );
document.write( " (v) <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=3x+%2B2+=+y%281-x%29 ALIGN=MIDDLE  ALT=\"3x+%2B2+=+y%281-x%29\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "divide by 1-x to get<BR>\n" );
document.write( "(vi) <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=%28%283x%2B2%29%2F%281-x%29%29+=+y%5E-1 ALIGN=MIDDLE  ALT=\"%28%283x%2B2%29%2F%281-x%29%29+=+y%5E-1\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "this is the inverse<BR>\n" );
document.write( "----<BR>\n" );
document.write( "a). domain of f(x) is all reals except x = -3<BR>\n" );
document.write( "The range of f^(-1)(x) is all reals except y = -3<BR>\n" );
document.write( "b). The range of f(x) is all reals except y = 1<BR>\n" );
document.write( "the domain of f^(-1)(x) is all reals except  x = 1 </SPAN>\n" );
document.write( "</TD></TR></TABLE>\n" );