document.write( "<A HREF=/cgi-bin/jump-to-question.mpl?question=1122381>Question 1122381</A>: <I><SPAN STYLE=\"word-break: break-all;\"> Find&#8203; f(g(x)) and&#8203; g(f(x)). State the domain of each.\r<BR>\n" );
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document.write( "f(x)= 7x+8; g(x)= x-3\r<BR>\n" );
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document.write( "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 #738500 by </B><A HREF=/tutors/aboutme.mpl?userid=Alex.33><B>Alex.33(110)</B></A><img src=\"/images/stars/stars-09.gif\" alt=\"\" >&nbsp;<A HREF=/tutors/aboutme.mpl?userid=Alex.33><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=Alex.33><BR>You can <A HREF=\"/cgi-bin/embed-solution.mpl?show=1&solution=738500\">put this solution on YOUR website!</A><BR><SPAN STYLE=\"word-break: break-all;\"> Assume that the original domains of f(x) and g(x) are all rational numbers(set R).<BR>\n" );
document.write( "f(g(x))=7(x-3)+8=7x-13. <BR>\n" );
document.write( "Methodogy:<BR>\n" );
document.write( "since g(x) is the independent variable in the outer f(x), its range, which when in its original domain R is R, need to be in the domain of f(x), which is also R. There's no problem when we just retain the domain of the inner g(x), R.<BR>\n" );
document.write( "The domain is R.<BR>\n" );
document.write( "g(f(x))=(7x+8)-3=7x+5.<BR>\n" );
document.write( "Apply the same algorithm. The domain is R.<BR>\n" );
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