document.write( "<A HREF=/cgi-bin/jump-to-question.mpl?question=144971>Question 144971</A>: <I><SPAN STYLE=\"word-break: break-all;\"> Over the set of real numbers, what is the domain of the composite function G(F(x))?\r<BR>\n" );
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document.write( "F(x) = 3 - x, G(y) = &#8730;y\r<BR>\n" );
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document.write( "G(F(x)) = &#8730;3-x\r<BR>\n" );
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document.write( "possible awnsers are:\r<BR>\n" );
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document.write( "   A. x > 3 <BR>\n" );
document.write( "   B. x  3 <BR>\n" );
document.write( "   C. x  3 <BR>\n" );
document.write( "   D. All real numbers \r<BR>\n" );
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document.write( " </SPAN>\n" );
document.write( "</I><HR><TABLE width=100%><TR><TD><B><A HREF=http://www.algebra.com/>Algebra.Com's</A> Answer #105648 by </B><A HREF=/tutors/aboutme.mpl?userid=solver91311><B>solver91311(24713)</B></A><img src=\"/images/stars/stars-13.gif\" alt=\"\" >&nbsp;<A HREF=/tutors/aboutme.mpl?userid=solver91311><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=solver91311><BR>You can <A HREF=\"/cgi-bin/embed-solution.mpl?show=1&solution=105648\">put this solution on YOUR website!</A><BR><SPAN STYLE=\"word-break: break-all;\"> The domain of F is all reals because there are no real values of x that would make F undefined.  G, on the other hand, requires that <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=y%3E=0 ALIGN=MIDDLE  ALT=\"y%3E=0\"   DISABLED_style= \"max-width:90%; height:auto;\" >.  Saying G(F(x)) is the same as saying <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=y=F%28x%29=3-x ALIGN=MIDDLE  ALT=\"y=F%28x%29=3-x\"   DISABLED_style= \"max-width:90%; height:auto;\" >, so the question becomes 'What values of x make y less than 0?'\r<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=3-x%3C0 ALIGN=MIDDLE  ALT=\"3-x%3C0\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=-x%3C-3 ALIGN=MIDDLE  ALT=\"-x%3C-3\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=x%3E3 ALIGN=MIDDLE  ALT=\"x%3E3\"   DISABLED_style= \"max-width:90%; height:auto;\" >\r<BR>\n" );
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document.write( "So anytime <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=x%3E3 ALIGN=MIDDLE  ALT=\"x%3E3\"   DISABLED_style= \"max-width:90%; height:auto;\" >, <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=y%3C0 ALIGN=MIDDLE  ALT=\"y%3C0\"   DISABLED_style= \"max-width:90%; height:auto;\" > and G would be undefined.  Therefore the domain of G(F(x)) is <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=x%3C=3 ALIGN=MIDDLE  ALT=\"x%3C=3\"   DISABLED_style= \"max-width:90%; height:auto;\" >.  In interval notation: <big><b> (<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=infinity ALIGN=MIDDLE  ALT=\"infinity\"   DISABLED_style= \"max-width:90%; height:auto;\" >,<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=3 ALIGN=MIDDLE  ALT=\"3\"   DISABLED_style= \"max-width:90%; height:auto;\" >] </big></b> </SPAN>\n" );
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