document.write( "<A HREF=/cgi-bin/jump-to-question.mpl?question=1110100>Question 1110100</A>: <I><SPAN STYLE=\"word-break: break-all;\"> The one-to-one function f is defined below.<BR>\n" );
document.write( "=f(x)=x/5x-4<BR>\n" );
document.write( "Find f^-1, where f^-1 is the inverse of f<BR>\n" );
document.write( ". <BR>\n" );
document.write( "Also state the domain and range of f^-1 in interval notation.<BR>\n" );
document.write( " </SPAN>\n" );
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document.write( "The domain of f(x) is all values except 4/5.<br><BR>\n" );
document.write( "That means the range of f^-1(x) is all values except 4/5.<br><BR>\n" );
document.write( "To find f^-1(x), switch x and y in the given function and solve for the new y.<br><BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=x+=+y%2F%285y-4%29 ALIGN=MIDDLE  ALT=\"x+=+y%2F%285y-4%29\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=x%285y-4%29+=+y ALIGN=MIDDLE  ALT=\"x%285y-4%29+=+y\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=5xy-4x+=+y ALIGN=MIDDLE  ALT=\"5xy-4x+=+y\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=5xy-y+=+4x ALIGN=MIDDLE  ALT=\"5xy-y+=+4x\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=%285x-1%29y+=+4x ALIGN=MIDDLE  ALT=\"%285x-1%29y+=+4x\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=y+=+4x%2F%285x-1%29 ALIGN=MIDDLE  ALT=\"y+=+4x%2F%285x-1%29\"   DISABLED_style= \"max-width:90%; height:auto;\" ><br><BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=f%5E-1%28x%29+=+%284x%29%2F%285x-1%29 ALIGN=MIDDLE  ALT=\"f%5E-1%28x%29+=+%284x%29%2F%285x-1%29\"   DISABLED_style= \"max-width:90%; height:auto;\" ><br><BR>\n" );
document.write( "The domain of f^-1(x) is all values except 1/5.<br><BR>\n" );
document.write( "Graphing the function and the inverse confirm these results.<br><BR>\n" );
document.write( "The graph of f(x) (red) has a vertical asymptote at x=4/5 and a horizontal asymptote at y=1/5 (green).<br><BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=graph%28400%2C400%2C-2%2C2%2C-2%2C2%2Cx%2F%285x-4%29%2C1%2F5%29 ALIGN=MIDDLE  ALT=\"graph%28400%2C400%2C-2%2C2%2C-2%2C2%2Cx%2F%285x-4%29%2C1%2F5%29\"   DISABLED_style= \"max-width:90%; height:auto;\" ><br><BR>\n" );
document.write( "The graph of f^-1(x) (red) has a vertical asymptote at x=1/5 and a horizontal asymptote at y = 4/5 (green).<br><BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=graph%28400%2C400%2C-2%2C2%2C-2%2C2%2C%284x%29%2F%285x-1%29%2C4%2F5%29 ALIGN=MIDDLE  ALT=\"graph%28400%2C400%2C-2%2C2%2C-2%2C2%2C%284x%29%2F%285x-1%29%2C4%2F5%29\"   DISABLED_style= \"max-width:90%; height:auto;\" ><br><BR>\n" );
document.write( "ANSWER:<BR>\n" );
document.write( "f^-1(x) = 4x/(5x-1)<BR>\n" );
document.write( "Domain: x not = 1/5<BR>\n" );
document.write( "Range: y not = 4/5 </SPAN>\n" );
document.write( "</TD></TR></TABLE>\n" );