document.write( "<A HREF=/cgi-bin/jump-to-question.mpl?question=30626>Question 30626</A>: <I><SPAN STYLE=\"word-break: break-all;\"> If f(x)=x^2-x and g(x)=-3+x find the following:<BR>\n" );
document.write( "(a) f(g(x))  (b)  g(f(x))  (c) f(f(-1))  (d) g(g(-3)) </SPAN>\n" );
document.write( "</I><HR><TABLE width=100%><TR><TD><B><A HREF=http://www.algebra.com/>Algebra.Com's</A> Answer #17360 by </B><A HREF=/tutors/aboutme.mpl?userid=sdmmadam@yahoo.com><B>sdmmadam@yahoo.com(530)</B></A><img src=\"/images/stars/stars-10.gif\" alt=\"\" >&nbsp;<A HREF=/tutors/aboutme.mpl?userid=sdmmadam@yahoo.com><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=17360\">put this solution on YOUR website!</A><BR><SPAN STYLE=\"word-break: break-all;\"> If f(x)=x^2-x and g(x)=-3+x find the following:<BR>\n" );
document.write( "(a) f(g(x))  (b)  g(f(x))  (c) f(f(-1))  (d) g(g(-3))\r<BR>\n" );
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document.write( "f(x)=x^2-x ----(1)<BR>\n" );
document.write( "g(x)=-3+x  ----(2)\r<BR>\n" );
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document.write( "(a) f(g(x)) = f(-3+x) using (2)<BR>\n" );
document.write( "= f(x-3)  (using additive commutativity we have (-3+x)= (x-3)  )<BR>\n" );
document.write( "=f(t) where t = (x-3)----(*)<BR>\n" );
document.write( "= t^2-t  using (1)<BR>\n" );
document.write( "= (x-3)^2-(x-3)using(*)<BR>\n" );
document.write( "=x^2-6x+9-x+3<BR>\n" );
document.write( "=x^2-6x-x+9+3<BR>\n" );
document.write( "=x^2-7x+12\r<BR>\n" );
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document.write( "b)g(f(x)) = g(x^2-x) using (1)<BR>\n" );
document.write( "=g(u)  where u = x^2-x  ----(**)<BR>\n" );
document.write( "= -3+u   using (2)<BR>\n" );
document.write( "= -3+ (x^2-x) using(**)<BR>\n" );
document.write( "= x^2-x-3\r<BR>\n" );
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document.write( "c) f(f(-1))  <BR>\n" );
document.write( "= f[(-1)^2-(-1)]  (using x = -1 in (1)which is f(x)=(x^2-x))<BR>\n" );
document.write( "=f[1+1]<BR>\n" );
document.write( "=f(2)<BR>\n" );
document.write( "= [(2)^2-(2)]  (using x = 2 in (1)which is f(x)=(x^2-x))<BR>\n" );
document.write( "= 4-2<BR>\n" );
document.write( "=2\r<BR>\n" );
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document.write( "(d) g(g(-3))<BR>\n" );
document.write( "= g[-3+(-3)] using x = -3 in (2) which is g(x) = -3+x )<BR>\n" );
document.write( "=g(-3-3)<BR>\n" );
document.write( "=g(-6)<BR>\n" );
document.write( "=[-3+(-6)]  using x = -6 in (2) which is g(x) = -3+x )<BR>\n" );
document.write( "= (-3-6)<BR>\n" );
document.write( "= -9\r<BR>\n" );
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document.write( "Answer: a)f(g(x)) = x^2-7x+12<BR>\n" );
document.write( "b)g(f(x)) = x^2-x-3<BR>\n" );
document.write( "c) f(f(-1))=2 <BR>\n" );
document.write( "(d) g(g(-3))= -9\r<BR>\n" );
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document.write( " </SPAN>\n" );
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