document.write( "<A HREF=/cgi-bin/jump-to-question.mpl?question=1021436>Question 1021436</A>: <I><SPAN STYLE=\"word-break: break-all;\"> Please show work.	<BR>\n" );
document.write( "Consider the functions:<BR>\n" );
document.write( "f(x)=x^2+4<BR>\n" );
document.write( "g(x)=x\r<BR>\n" );
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document.write( "a.	find f(2g(x))\r<BR>\n" );
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document.write( "b.	What is the inverse of f(x)?\r<BR>\n" );
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document.write( "c.	What is the inverse of g(x)?<BR>\n" );
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document.write( "</I><HR><TABLE width=100%><TR><TD><B><A HREF=http://www.algebra.com/>Algebra.Com's</A> Answer #637214 by </B><A HREF=/tutors/aboutme.mpl?userid=fractalier><B>fractalier(6550)</B></A><img src=\"/images/stars/stars-13.gif\" alt=\"\" >&nbsp;<A HREF=/tutors/aboutme.mpl?userid=fractalier><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=fractalier><BR>You can <A HREF=\"/cgi-bin/embed-solution.mpl?show=1&solution=637214\">put this solution on YOUR website!</A><BR><SPAN STYLE=\"word-break: break-all;\"> a)  If g(x) = x, then 2g(x) = 2x and then f(2g(x)) = f(2x) = (2x)^2 + 4 = 4x^2 + 4<BR>\n" );
document.write( "b)  To find an inverse, put y in for f(x).  You switch x for y and solve for the new y.  Then put f^-1(x) in for the new y.  Like this<BR>\n" );
document.write( "y = x^2 + 4<BR>\n" );
document.write( "x = y^2 + 4<BR>\n" );
document.write( "x - 4 = y^2<BR>\n" );
document.write( "y = sqrt(x-4)<BR>\n" );
document.write( "f^-1(x) = sqrt(x-4)<BR>\n" );
document.write( "c)  g(x) = x<BR>\n" );
document.write( "y = x<BR>\n" );
document.write( "x = y<BR>\n" );
document.write( "f^-1(x) = x <BR>\n" );
document.write( "No surprise.<BR>\n" );
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