document.write( "<A HREF=/cgi-bin/jump-to-question.mpl?question=1170514>Question 1170514</A>: <I><SPAN STYLE=\"word-break: break-all;\"> Functions f and g are given by<BR>\n" );
document.write( "f(x)=12x−7 and g(x)=123x−41\r<BR>\n" );
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document.write( "Simplify (f∘g)(x).\r<BR>\n" );
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document.write( "(f∘g)(x)=<BR>\n" );
document.write( "List the numbers that are NOT in the domain of f∘g in a comma separated list. </SPAN>\n" );
document.write( "</I><HR><TABLE width=100%><TR><TD><B><A HREF=http://www.algebra.com/>Algebra.Com's</A> Answer #851166 by </B><A HREF=/tutors/aboutme.mpl?userid=CPhill><B>CPhill(1959)</B></A><img src=\"/images/stars/stars-12.gif\" alt=\"\" >&nbsp;<A HREF=/tutors/aboutme.mpl?userid=CPhill><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=CPhill><BR>You can <A HREF=\"/cgi-bin/embed-solution.mpl?show=1&solution=851166\">put this solution on YOUR website!</A><BR><SPAN STYLE=\"word-break: break-all;\"> Let's find (f∘g)(x) and its domain.\r<BR>\n" );
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document.write( "**1. Find (f∘g)(x)**\r<BR>\n" );
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document.write( "(f∘g)(x) = f(g(x))\r<BR>\n" );
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document.write( "We have:<BR>\n" );
document.write( "f(x) = 12x - 7<BR>\n" );
document.write( "g(x) = 123x - 41\r<BR>\n" );
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document.write( "Substitute g(x) into f(x):<BR>\n" );
document.write( "(f∘g)(x) = f(123x - 41)<BR>\n" );
document.write( "(f∘g)(x) = 12(123x - 41) - 7<BR>\n" );
document.write( "(f∘g)(x) = (12 * 123)x - (12 * 41) - 7<BR>\n" );
document.write( "(f∘g)(x) = 1476x - 492 - 7<BR>\n" );
document.write( "(f∘g)(x) = 1476x - 499\r<BR>\n" );
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document.write( "**2. Find the Domain of (f∘g)(x)**\r<BR>\n" );
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document.write( "* The domain of f(x) = 12x - 7 is all real numbers, since it's a linear function.<BR>\n" );
document.write( "* The domain of g(x) = 123x - 41 is also all real numbers, since it's a linear function.<BR>\n" );
document.write( "* The composition (f∘g)(x) = 1476x - 499 is also a linear function, so its domain is all real numbers.\r<BR>\n" );
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document.write( "Since both f(x) and g(x) have a domain of all real numbers, the composition (f∘g)(x) also has a domain of all real numbers.\r<BR>\n" );
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document.write( "**3. List Numbers NOT in the Domain**\r<BR>\n" );
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document.write( "Since the domain of (f∘g)(x) is all real numbers, there are no numbers excluded from the domain.\r<BR>\n" );
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document.write( "**Answer:**\r<BR>\n" );
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document.write( "(f∘g)(x) = 1476x - 499\r<BR>\n" );
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document.write( "List the numbers that are NOT in the domain of f∘g in a comma separated list: None<BR>\n" );
document.write( " </SPAN>\n" );
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