document.write( "<A HREF=/cgi-bin/jump-to-question.mpl?question=31419>Question 31419</A>: <I><SPAN STYLE=\"word-break: break-all;\"> if f(x) = x-1 and g(x) = x^2 +1 find:<BR>\n" );
document.write( "1. g(5)<BR>\n" );
document.write( "2. f(g(5))<BR>\n" );
document.write( "3. f(g(x))<BR>\n" );
document.write( "4. g(f(x))<BR>\n" );
document.write( "5. find all values of x for which f(g(x)) = g(f(x)) </SPAN>\n" );
document.write( "</I><HR><TABLE width=100%><TR><TD><B><A HREF=http://www.algebra.com/>Algebra.Com's</A> Answer #18171 by </B><A HREF=/tutors/aboutme.mpl?userid=mukhopadhyay><B>mukhopadhyay(490)</B></A><img src=\"/images/stars/stars-10.gif\" alt=\"\" >&nbsp;<A HREF=/tutors/aboutme.mpl?userid=mukhopadhyay><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=18171\">put this solution on YOUR website!</A><BR><SPAN STYLE=\"word-break: break-all;\"> 1. g(5) = 5^2+1 = 26<BR>\n" );
document.write( "2. f(g(5)) = f(26) = 26-1 = 25<BR>\n" );
document.write( "3. f(g(x)) = f(x^2+1) = x^2+1-1 = x^2<BR>\n" );
document.write( "4. g(f(x)) = g(x-1) = (x-1)^2+1 = x^2-2x+1+1 = x^2-2x+2<BR>\n" );
document.write( "5. find all values of x for which f(g(x)) = g(f(x)):<BR>\n" );
document.write( "f(g(x)) = g(f(x)) <BR>\n" );
document.write( "=>x^2 = x^2-2x+2<BR>\n" );
document.write( "=>2x = 2<BR>\n" );
document.write( "=>x = 1\r<BR>\n" );
document.write( "\n" );
document.write( "For x=1, f(g(x)) = g(f(x)) </SPAN>\n" );
document.write( "</TD></TR></TABLE>\n" );