document.write( "<A HREF=/cgi-bin/jump-to-question.mpl?question=1092562>Question 1092562</A>: <I><SPAN STYLE=\"word-break: break-all;\"> what is the inverse of f(x)=10/5x+2?<BR>\n" );
document.write( "and what is the domain and rage for both f(x) and 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 #707203 by </B><A HREF=/tutors/aboutme.mpl?userid=greenestamps><B>greenestamps(13200)</B></A><img src=\"/images/stars/stars-13.gif\" alt=\"\" >&nbsp;<A HREF=/tutors/aboutme.mpl?userid=greenestamps><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=greenestamps><BR>You can <A HREF=\"/cgi-bin/embed-solution.mpl?show=1&solution=707203\">put this solution on YOUR website!</A><BR><SPAN STYLE=\"word-break: break-all;\"> <br>One version of the standard way to find the inverse of a function is to switch the 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+=+10%2F5y+%2B+2 ALIGN=MIDDLE  ALT=\"x+=+10%2F5y+%2B+2\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=x-2+=+2%2Fy ALIGN=MIDDLE  ALT=\"x-2+=+2%2Fy\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=y+=+2%2F%28x-2%29 ALIGN=MIDDLE  ALT=\"y+=+2%2F%28x-2%29\"   DISABLED_style= \"max-width:90%; height:auto;\" ><br><BR>\n" );
document.write( "In the given function, 0 is excluded from the domain because it would make the denominator 0.  That means 0 is excluded from the range of the inverse function.<br><BR>\n" );
document.write( "You can also see that 0 is not in the range of the inverse function, because if you try to solve<BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=2%2F%28x-2%29+=+0 ALIGN=MIDDLE  ALT=\"2%2F%28x-2%29+=+0\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "you get no solution.<br><BR>\n" );
document.write( "Similarly you can see that 2 is excluded from the range of the given function, because, again, if you try to solve<BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=10%2F5y+%2B+2+=+2 ALIGN=MIDDLE  ALT=\"10%2F5y+%2B+2+=+2\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "you will get no solution.  And since 2 is excluded from the range of the given function, it is excluded from the domain of the inverse function.  And we can see that by looking at the inverse function, because x=2 would make the denominator 0.<br><BR>\n" );
document.write( "In summary...<br><BR>\n" );
document.write( "For the given function,<BR>\n" );
document.write( "Domain is x not equal to 0<BR>\n" );
document.write( "Range is y not equal to 2<br><BR>\n" );
document.write( "For the inverse function,<BR>\n" );
document.write( "Domain is x not equal to 2<BR>\n" );
document.write( "Range is y not equal to 0 </SPAN>\n" );
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