document.write( "<A HREF=/cgi-bin/jump-to-question.mpl?question=462903>Question 462903</A>: <I><SPAN STYLE=\"word-break: break-all;\"> Hello, quick question. I need to find the inverse of this function. And the domain and range of it. \r<BR>\n" );
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document.write( "f(x)= 3/x-7\r<BR>\n" );
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document.write( "This is the answer that I got, did I do anything wrong?<BR>\n" );
document.write( "Domain of f: (-infinity, 7)U(7, infinity)<BR>\n" );
document.write( "Range of f: (-infinity, 0)U(0, infinity)\r<BR>\n" );
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document.write( "f-1(x)= (3/x)+7<BR>\n" );
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document.write( "</I><HR><TABLE width=100%><TR><TD><B><A HREF=http://www.algebra.com/>Algebra.Com's</A> Answer #317256 by </B><A HREF=/tutors/aboutme.mpl?userid=jim_thompson5910><B>jim_thompson5910(35256)</B></A><img src=\"/images/stars/stars-13.gif\" alt=\"\" >&nbsp;<A HREF=/tutors/aboutme.mpl?userid=jim_thompson5910><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=317256\">put this solution on YOUR website!</A><BR><SPAN STYLE=\"word-break: break-all;\"> If the function is <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=f%28x%29=3%2F%28x-7%29 ALIGN=MIDDLE  ALT=\"f%28x%29=3%2F%28x-7%29\"   DISABLED_style= \"max-width:90%; height:auto;\" >, then replace f(x) with y, then swap x and y to get <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=x=3%2F%28y-7%29 ALIGN=MIDDLE  ALT=\"x=3%2F%28y-7%29\"   DISABLED_style= \"max-width:90%; height:auto;\" > and solve for y \r<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=x=3%2F%28y-7%29 ALIGN=MIDDLE  ALT=\"x=3%2F%28y-7%29\"   DISABLED_style= \"max-width:90%; height:auto;\" >\r<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=x%28y-7%29=3 ALIGN=MIDDLE  ALT=\"x%28y-7%29=3\"   DISABLED_style= \"max-width:90%; height:auto;\" >\r<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=y-7=3%2Fx ALIGN=MIDDLE  ALT=\"y-7=3%2Fx\"   DISABLED_style= \"max-width:90%; height:auto;\" >\r<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=y=3%2Fx%2B7 ALIGN=MIDDLE  ALT=\"y=3%2Fx%2B7\"   DISABLED_style= \"max-width:90%; height:auto;\" >\r<BR>\n" );
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document.write( "So the inverse function is <IMG STYLE=\"max-width:80%;\" SRC=\"/cgi-bin/rendertex.cgi?\LARGE f^{-1}(x)=\frac{3}{x}+7\">\r<BR>\n" );
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document.write( "Domain of f: <IMG STYLE=\"max-width:80%;\" SRC=\"/cgi-bin/rendertex.cgi?\LARGE \left(-\infty,7\right)\cup\left(7,\infty\right)\"> (ie you can plug in any number but 7 since this value results in a division by zero)\r<BR>\n" );
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document.write( "Range of f: <IMG STYLE=\"max-width:80%;\" SRC=\"/cgi-bin/rendertex.cgi?\LARGE \left(-\infty,0\right)\cup\left(0,\infty\right)\"> (this is equal to the horizontal asymptote)\r<BR>\n" );
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document.write( "Now simply flip the domain and range of f(x) to get the domain and range for the inverse <IMG STYLE=\"max-width:80%;\" SRC=\"/cgi-bin/rendertex.cgi?\LARGE f^{-1}(x)\">\r<BR>\n" );
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document.write( "Domain of <IMG STYLE=\"max-width:80%;\" SRC=\"/cgi-bin/rendertex.cgi?\LARGE f^{-1}(x)\">: <IMG STYLE=\"max-width:80%;\" SRC=\"/cgi-bin/rendertex.cgi?\LARGE \left(-\infty,0\right)\cup\left(0,\infty\right)\"> \r<BR>\n" );
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document.write( "Range of <IMG STYLE=\"max-width:80%;\" SRC=\"/cgi-bin/rendertex.cgi?\LARGE f^{-1}(x)\">: <IMG STYLE=\"max-width:80%;\" SRC=\"/cgi-bin/rendertex.cgi?\LARGE \left(-\infty,7\right)\cup\left(7,\infty\right)\">  </SPAN>\n" );
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