document.write( "<A HREF=/cgi-bin/jump-to-question.mpl?question=775839>Question 775839</A>: <I><SPAN STYLE=\"word-break: break-all;\"> Given the functions<BR>\n" );
document.write( "f(x)=1/x-3 ; g(x)=5x/x+4\r<BR>\n" );
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document.write( "Find<BR>\n" );
document.write( "a.f(5)+g(-3)\r<BR>\n" );
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document.write( "b.(f+g)(x)\r<BR>\n" );
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document.write( "c.(g&#8728;f)(x)\r<BR>\n" );
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document.write( "d.(f&#8728;g)(-2) 	 </SPAN>\n" );
document.write( "</I><HR><TABLE width=100%><TR><TD><B><A HREF=http://www.algebra.com/>Algebra.Com's</A> Answer #473200 by </B><A HREF=/tutors/aboutme.mpl?userid=tanjo3><B>tanjo3(60)</B></A><img src=\"/images/stars/stars-08.gif\" alt=\"\" >&nbsp;<A HREF=/tutors/aboutme.mpl?userid=tanjo3><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=473200\">put this solution on YOUR website!</A><BR><SPAN STYLE=\"word-break: break-all;\"> I will assume the functions are as follows:<BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=f%28x%29=1%2F%28x-3%29 ALIGN=MIDDLE  ALT=\"f%28x%29=1%2F%28x-3%29\"   DISABLED_style= \"max-width:90%; height:auto;\" >; <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=g%28x%29=5x%2F%28x%2B4%29 ALIGN=MIDDLE  ALT=\"g%28x%29=5x%2F%28x%2B4%29\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( " <BR>\n" );
document.write( "a. f(5) + g(-3)<BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=f%285%29=+1+%2F+%285-3%29 ALIGN=MIDDLE  ALT=\"f%285%29=+1+%2F+%285-3%29\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=f%285%29=+1%2F2 ALIGN=MIDDLE  ALT=\"f%285%29=+1%2F2\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( " <BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=g%28-3%29=+5%28-3%29+%2F+%28-3%2B4%29 ALIGN=MIDDLE  ALT=\"g%28-3%29=+5%28-3%29+%2F+%28-3%2B4%29\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=g%28-3%29=+-15 ALIGN=MIDDLE  ALT=\"g%28-3%29=+-15\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( " <BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=f%285%29+%2B+g%28-3%29+=+1%2F2+%2B+%28-15%29 ALIGN=MIDDLE  ALT=\"f%285%29+%2B+g%28-3%29+=+1%2F2+%2B+%28-15%29\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=f%285%29+%2B+g%28-3%29+=+1%2F2+%2B+%28-30%29+%2F+2 ALIGN=MIDDLE  ALT=\"f%285%29+%2B+g%28-3%29+=+1%2F2+%2B+%28-30%29+%2F+2\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=f%285%29+%2B+g%28-3%29+=+-29%2F2 ALIGN=MIDDLE  ALT=\"f%285%29+%2B+g%28-3%29+=+-29%2F2\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( " <BR>\n" );
document.write( "-------------------------------------------------------------------------------<BR>\n" );
document.write( " <BR>\n" );
document.write( "b. (f + g)(x)<BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=%28f+%2B+g%29%28x%29+=+f%28x%29+%2B+g%28x%29 ALIGN=MIDDLE  ALT=\"%28f+%2B+g%29%28x%29+=+f%28x%29+%2B+g%28x%29\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=%28f+%2B+g%29%28x%29+=+1%2F%28x-3%29+%2B+5x%2F%28x%2B4%29 ALIGN=MIDDLE  ALT=\"%28f+%2B+g%29%28x%29+=+1%2F%28x-3%29+%2B+5x%2F%28x%2B4%29\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=%28f+%2B+g%29%28x%29+=+%28%28x%2B4%29%2B%285x%29%28x-3%29%29+%2F+%28%28x-3%29%28x%2B4%29%29 ALIGN=MIDDLE  ALT=\"%28f+%2B+g%29%28x%29+=+%28%28x%2B4%29%2B%285x%29%28x-3%29%29+%2F+%28%28x-3%29%28x%2B4%29%29\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=%28f+%2B+g%29%28x%29+=+%285x%5E2+-+14x+%2B+4%29+%2F+%28x%5E2+%2B+x+-+12%29 ALIGN=MIDDLE  ALT=\"%28f+%2B+g%29%28x%29+=+%285x%5E2+-+14x+%2B+4%29+%2F+%28x%5E2+%2B+x+-+12%29\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( " <BR>\n" );
document.write( "-------------------------------------------------------------------------------<BR>\n" );
document.write( " <BR>\n" );
document.write( "c. (g &#8728; f)(x)<BR>\n" );
document.write( "(g &#8728; f)(x) = g(f(x))<BR>\n" );
document.write( "(g &#8728; f)(x) = g(1/(x-3)))<BR>\n" );
document.write( "(g &#8728; f)(x) = [5(1/(x-3))]/[(1/(x-3))+4]<BR>\n" );
document.write( "(g &#8728; f)(x) = [5/(x-3)]/[(1/(x-3))+((4(x-3))/(x-3))]<BR>\n" );
document.write( "(g &#8728; f)(x) = [5/(x-3)]/[(4x-11)/(x-3)]<BR>\n" );
document.write( "(g &#8728; f)(x) = (4x-11)/5<BR>\n" );
document.write( " <BR>\n" );
document.write( "Note: (g &#8728; f)(x) = (4x-11)/5 for x &#8800; 3<BR>\n" );
document.write( " <BR>\n" );
document.write( "-------------------------------------------------------------------------------<BR>\n" );
document.write( " <BR>\n" );
document.write( "d. (f &#8728; g)(-2)<BR>\n" );
document.write( "(f &#8728; g)(-2) = f(g(-2))<BR>\n" );
document.write( " <BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=g%28-2%29=+5%28-2%29+%2F+%28-2%2B4%29 ALIGN=MIDDLE  ALT=\"g%28-2%29=+5%28-2%29+%2F+%28-2%2B4%29\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=g%28-3%29=+%28-10%29+%2F+2 ALIGN=MIDDLE  ALT=\"g%28-3%29=+%28-10%29+%2F+2\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=g%28-3%29=+-5 ALIGN=MIDDLE  ALT=\"g%28-3%29=+-5\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( " <BR>\n" );
document.write( "(f &#8728; g)(-2) = f(-5)<BR>\n" );
document.write( "(f &#8728; g)(-2) = 1 / (-5-3)<BR>\n" );
document.write( "(f &#8728; g)(-2) = -1/8 </SPAN>\n" );
document.write( "</TD></TR></TABLE>\n" );