document.write( "<A HREF=/cgi-bin/jump-to-question.mpl?question=198357>Question 198357</A>: <I><SPAN STYLE=\"word-break: break-all;\"> Hello!\r<BR>\n" );
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document.write( "Find the inverse function of f.<BR>\n" );
document.write( "f(x) = -3 + &#8730;-9+ 6x \r<BR>\n" );
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document.write( "thanks for your help! </SPAN>\n" );
document.write( "</I><HR><TABLE width=100%><TR><TD><B><A HREF=http://www.algebra.com/>Algebra.Com's</A> Answer #148840 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=148840\">put this solution on YOUR website!</A><BR><SPAN STYLE=\"word-break: break-all;\"> I'm assuming that the function is <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=f%28x%29=-3%2Bsqrt%28-9%2B6x%29 ALIGN=MIDDLE  ALT=\"f%28x%29=-3%2Bsqrt%28-9%2B6x%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=f%28x%29=-3%2Bsqrt%28-9%2B6x%29 ALIGN=MIDDLE  ALT=\"f%28x%29=-3%2Bsqrt%28-9%2B6x%29\"   DISABLED_style= \"max-width:90%; height:auto;\" > Start with the given function.\r<BR>\n" );
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document.write( "Take note that the domain is <font size=\"8\">[</font><IMG STYLE=\"max-width:80%;\" SRC=\"/cgi-bin/rendertex.cgi?\LARGE \frac{3}{2},\infty\"><font size=\"8\">)</font> and the range is <font size=\"8\">[</font><IMG STYLE=\"max-width:80%;\" SRC=\"/cgi-bin/rendertex.cgi?\LARGE -3,\infty\"><font size=\"8\">)</font> (graph the function if you are not sure)\r<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=y=-3%2Bsqrt%28-9%2B6x%29 ALIGN=MIDDLE  ALT=\"y=-3%2Bsqrt%28-9%2B6x%29\"   DISABLED_style= \"max-width:90%; height:auto;\" > Replace f(x) with y\r<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=x=-3%2Bsqrt%28-9%2B6y%29 ALIGN=MIDDLE  ALT=\"x=-3%2Bsqrt%28-9%2B6y%29\"   DISABLED_style= \"max-width:90%; height:auto;\" > Swap each x and y. The goal now is to solve for y to find the inverse.\r<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=x%2B3=sqrt%28-9%2B6y%29 ALIGN=MIDDLE  ALT=\"x%2B3=sqrt%28-9%2B6y%29\"   DISABLED_style= \"max-width:90%; height:auto;\" > Add 3 to both sides.\r<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=%28x%2B3%29%5E2=%28sqrt%28-9%2B6y%29%29%5E2 ALIGN=MIDDLE  ALT=\"%28x%2B3%29%5E2=%28sqrt%28-9%2B6y%29%29%5E2\"   DISABLED_style= \"max-width:90%; height:auto;\" > Square both sides (to undo the square root)\r<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=%28x%2B3%29%5E2=-9%2B6y ALIGN=MIDDLE  ALT=\"%28x%2B3%29%5E2=-9%2B6y\"   DISABLED_style= \"max-width:90%; height:auto;\" > Square the square root to eliminate it.\r<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=x%5E2%2B6x%2B9=-9%2B6y ALIGN=MIDDLE  ALT=\"x%5E2%2B6x%2B9=-9%2B6y\"   DISABLED_style= \"max-width:90%; height:auto;\" > FOIL\r<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=x%5E2%2B6x%2B9%2B9=6y ALIGN=MIDDLE  ALT=\"x%5E2%2B6x%2B9%2B9=6y\"   DISABLED_style= \"max-width:90%; height:auto;\" > Add 9 to both sides.\r<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=x%5E2%2B6x%2B18=6y ALIGN=MIDDLE  ALT=\"x%5E2%2B6x%2B18=6y\"   DISABLED_style= \"max-width:90%; height:auto;\" > Combine like terms.\r<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=%28x%5E2%2B6x%2B18%29%2F6=y ALIGN=MIDDLE  ALT=\"%28x%5E2%2B6x%2B18%29%2F6=y\"   DISABLED_style= \"max-width:90%; height:auto;\" > Divide both sides by 6.\r<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=y=%28x%5E2%2B6x%2B18%29%2F6 ALIGN=MIDDLE  ALT=\"y=%28x%5E2%2B6x%2B18%29%2F6\"   DISABLED_style= \"max-width:90%; height:auto;\" > Rearrange the equation.\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{x^2+6x+18}{6}\">\r<BR>\n" );
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document.write( "Now because the domain and range for f(x) was <font size=\"8\">[</font><IMG STYLE=\"max-width:80%;\" SRC=\"/cgi-bin/rendertex.cgi?\LARGE \frac{3}{2},\infty\"><font size=\"8\">)</font> and the range is <font size=\"8\">[</font><IMG STYLE=\"max-width:80%;\" SRC=\"/cgi-bin/rendertex.cgi?\LARGE -3,\infty\"><font size=\"8\">)</font>, this means that the domain and range for the inverse are:\r<BR>\n" );
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document.write( "Domain: <font size=\"8\">[</font><IMG STYLE=\"max-width:80%;\" SRC=\"/cgi-bin/rendertex.cgi?\LARGE -3,\infty\"><font size=\"8\">)</font> \r<BR>\n" );
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document.write( "Range: <font size=\"8\">[</font><IMG STYLE=\"max-width:80%;\" SRC=\"/cgi-bin/rendertex.cgi?\LARGE \frac{3}{2},\infty\"><font size=\"8\">)</font> </SPAN>\n" );
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