document.write( "<A HREF=/cgi-bin/jump-to-question.mpl?question=118159>Question 118159</A>: <I><SPAN STYLE=\"word-break: break-all;\"> f(x)= (-2 over x+5) -1<BR>\n" );
document.write( "g(x)= x-2\r<BR>\n" );
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document.write( "determine the composite function f(g(x)), and then find the inverse of that function. state domain and range. then graph the composite function and its inverse.\r<BR>\n" );
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document.write( " PLEASE HELP ME THIS WILL PRACTICALLY CHANGE MY LIFE IF YOU CAN HELP ME.<BR>\n" );
document.write( "thank you for helping me, you are the greatest!!!! </SPAN>\n" );
document.write( "</I><HR><TABLE width=100%><TR><TD><B><A HREF=http://www.algebra.com/>Algebra.Com's</A> Answer #86269 by </B><A HREF=/tutors/aboutme.mpl?userid=Fombitz><B>Fombitz(32388)</B></A><img src=\"/images/stars/stars-13.gif\" alt=\"\" >&nbsp;<A HREF=/tutors/aboutme.mpl?userid=Fombitz><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=Fombitz><BR>You can <A HREF=\"/cgi-bin/embed-solution.mpl?show=1&solution=86269\">put this solution on YOUR website!</A><BR><SPAN STYLE=\"word-break: break-all;\"> Change your life?<BR>\n" );
document.write( "As long as there's no pressure. <BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=f%28x%29=%28-2%29%2F%28x%2B5%29-1 ALIGN=MIDDLE  ALT=\"f%28x%29=%28-2%29%2F%28x%2B5%29-1\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=g%28x%29=x-2 ALIGN=MIDDLE  ALT=\"g%28x%29=x-2\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "To find the composite f(g(x)), substitute (x-2) where there is an x in f(x).<BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=f%28g%28x%29%29=%28-2%29%2F%28%28x-2%29%2B5%29-1 ALIGN=MIDDLE  ALT=\"f%28g%28x%29%29=%28-2%29%2F%28%28x-2%29%2B5%29-1\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=f%28g%28x%29%29=%28-2%29%2F%28x%2B3%29-1 ALIGN=MIDDLE  ALT=\"f%28g%28x%29%29=%28-2%29%2F%28x%2B3%29-1\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "The domain of f(g(x)) is all points except x=-3, since the denominator goes to zero.<BR>\n" );
document.write( "For the range of f(x), as x gets large, either positive or negative, the term (-2)/(x+3) goes to zero and<BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=f%28x%29-%3E-1 ALIGN=MIDDLE  ALT=\"f%28x%29-%3E-1\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "Here is the graph of f(g(x)).<BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=+graph%28+300%2C+300%2C+-20%2C+20%2C+-5%2C+5%2C%28-2%29%2F%28x%2B3%29-1%29+ ALIGN=MIDDLE  ALT=\"+graph%28+300%2C+300%2C+-20%2C+20%2C+-5%2C+5%2C%28-2%29%2F%28x%2B3%29-1%29+\"   DISABLED_style= \"max-width:90%; height:auto;\" > <BR>\n" );
document.write( "That was f(g(x)).<BR>\n" );
document.write( "Now for the inverse. <BR>\n" );
document.write( "To find the inverse of <BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=y=%28-2%29%2F%28x%2B3%29-1 ALIGN=MIDDLE  ALT=\"y=%28-2%29%2F%28x%2B3%29-1\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "Reverse x and y and solve for y.<BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=y=%28-2%29%2F%28x%2B3%29-1 ALIGN=MIDDLE  ALT=\"y=%28-2%29%2F%28x%2B3%29-1\"   DISABLED_style= \"max-width:90%; height:auto;\" > Original equation of f(g(x)).<BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=highlight%28x%29=%28-2%29%2F%28highlight%28y%29%2B3%29-1 ALIGN=MIDDLE  ALT=\"highlight%28x%29=%28-2%29%2F%28highlight%28y%29%2B3%29-1\"   DISABLED_style= \"max-width:90%; height:auto;\" > Interchange x and y.<BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=x%28y%2B3%29=-2-%28y%2B3%29 ALIGN=MIDDLE  ALT=\"x%28y%2B3%29=-2-%28y%2B3%29\"   DISABLED_style= \"max-width:90%; height:auto;\" > Multiply both sides by (y+3).<BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=xy%2B3x=-2-y-3 ALIGN=MIDDLE  ALT=\"xy%2B3x=-2-y-3\"   DISABLED_style= \"max-width:90%; height:auto;\" > Distributive property.<BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=xy%2B3x=-y-5 ALIGN=MIDDLE  ALT=\"xy%2B3x=-y-5\"   DISABLED_style= \"max-width:90%; height:auto;\" > Simplify.<BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=xy%2By=-3x-5 ALIGN=MIDDLE  ALT=\"xy%2By=-3x-5\"   DISABLED_style= \"max-width:90%; height:auto;\" > Group like terms (y on left, x on right).<BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=y%28x%2B1%29=-%283x%2B5%29 ALIGN=MIDDLE  ALT=\"y%28x%2B1%29=-%283x%2B5%29\"   DISABLED_style= \"max-width:90%; height:auto;\" >Distributive property.<BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=y=-%283x%2B5%29%2F%28x%2B1%29 ALIGN=MIDDLE  ALT=\"y=-%283x%2B5%29%2F%28x%2B1%29\"   DISABLED_style= \"max-width:90%; height:auto;\" >Divide by (x+1).<BR>\n" );
document.write( "There it is. <BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=f%28g%28x%29%29%5E-1=-%283x%2B5%29%2F%28x%2B1%29 ALIGN=MIDDLE  ALT=\"f%28g%28x%29%29%5E-1=-%283x%2B5%29%2F%28x%2B1%29\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "Domain of the inverse function is all numbers except x=-1. <BR>\n" );
document.write( "Think about the range of f(g(x)) and the domain of the inverse and you'll see why. <BR>\n" );
document.write( "Hint : You never reach -1 in f(g(x)) except at <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=infinity ALIGN=MIDDLE  ALT=\"infinity\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "Range of the inverse function: as x gets large, the inverse function looks like,<BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=y=-%283x%2Fx%29=-%283cross%28x%29%2Fcross%28x%29%29=-3 ALIGN=MIDDLE  ALT=\"y=-%283x%2Fx%29=-%283cross%28x%29%2Fcross%28x%29%29=-3\"   DISABLED_style= \"max-width:90%; height:auto;\" > <BR>\n" );
document.write( "Again think about the range of the inverse and the domain of the f(g(x)) for reasons why. <BR>\n" );
document.write( "Here's the graph of the inverse. <BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=+graph%28+300%2C+300%2C+-5%2C+5%2C+-5%2C+5%2C-%283x%2B5%29%2F%28x%2B1%29%29 ALIGN=MIDDLE  ALT=\"+graph%28+300%2C+300%2C+-5%2C+5%2C+-5%2C+5%2C-%283x%2B5%29%2F%28x%2B1%29%29\"   DISABLED_style= \"max-width:90%; height:auto;\" > </SPAN>\n" );
document.write( "</TD></TR></TABLE>\n" );