document.write( "<A HREF=/cgi-bin/jump-to-question.mpl?question=455322>Question 455322</A>: <I><SPAN STYLE=\"word-break: break-all;\"> What does it mean to \"find the domain and range of the composition f of g? and to write the answer in \"set notation\" ??? Thank you </SPAN>\n" );
document.write( "</I><HR><TABLE width=100%><TR><TD><B><A HREF=http://www.algebra.com/>Algebra.Com's</A> Answer #312600 by </B><A HREF=/tutors/aboutme.mpl?userid=stanbon><B>stanbon(75887)</B></A><img src=\"/images/stars/stars-13.gif\" alt=\"\" >&nbsp;<A HREF=/tutors/aboutme.mpl?userid=stanbon><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=312600\">put this solution on YOUR website!</A><BR><SPAN STYLE=\"word-break: break-all;\"> What does it mean to \"find the domain and range of the composition f of g? and to write the answer in \"set notation\" ??? <BR>\n" );
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document.write( "A function is a machine.  You feed it \"x\" and<BR>\n" );
document.write( "it gives you f(x).<BR>\n" );
document.write( "Now, if you feed f(x) to another machine, g,<BR>\n" );
document.write( "you will get g[f(x)]<BR>\n" );
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document.write( "That is what composition is.  It's two machines<BR>\n" );
document.write( "operating one after another.<BR>\n" );
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document.write( "Example:<BR>\n" );
document.write( "f(x) = x+3<BR>\n" );
document.write( "g(x) = 2x<BR>\n" );
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document.write( "fog(x) = f[g(x)] = f[2x] = 2x+3<BR>\n" );
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document.write( "OR<BR>\n" );
document.write( "gof(x) = g[f(x)] = g[x+3] = 2(x+3) = 2x+6<BR>\n" );
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document.write( "If an answer happens to be x = 2, or x = 3<BR>\n" );
document.write( "the set notation would look like {x | x = 2 or x = 3}<BR>\n" );
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document.write( "Cheers,<BR>\n" );
document.write( "Stan H. </SPAN>\n" );
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