document.write( "<A HREF=/cgi-bin/jump-to-question.mpl?question=210295>Question 210295</A>: <I><SPAN STYLE=\"word-break: break-all;\"> Hi all, Im having trouble with the following Function and Domain problem. I have already asked and been given responses and answers for questions a) and b) but was hoping to get some help with the c) questions. (See below) <BR>\n" );
document.write( "The function f is defined by y = f(x) = 2 ln 4x, 0:01 <= x >= 1. <BR>\n" );
document.write( "(a) Solve for x in terms of y, and hence and the formula for the inverse<BR>\n" );
document.write( "function f^(-1)(x). Answer: y = (1/4)e^(x/2)<BR>\n" );
document.write( "b) Write down the domain of f^(-1) Answer: Since the Range of y = 2*ln(4x) is f(0.01) which is -6.438 < y < 2.7726 the Domain of f^-1(x) is -6.438 < x <= 2.7726 <BR>\n" );
document.write( "c) Plot f from x = 0:01 to x = 1 and then plot f^(-1) on the same axes but only for domain values of x given by the range of f.<BR>\n" );
document.write( "Help with c would be most appreciated.<BR>\n" );
document.write( "-Nick.\r<BR>\n" );
document.write( "<BR>\n" );
document.write( "<BR>\n" );
document.write( "\n" );
document.write( " </SPAN>\n" );
document.write( "</I><HR><TABLE width=100%><TR><TD><B><A HREF=http://www.algebra.com/>Algebra.Com's</A> Answer #158883 by </B><A HREF=/tutors/aboutme.mpl?userid=stanbon><B>stanbon(75887)</B></A><img src=\"/images/stars/stars-13.gif\" alt=\"\" >&nbsp;<A HREF=/tutors/aboutme.mpl?userid=stanbon><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=158883\">put this solution on YOUR website!</A><BR><SPAN STYLE=\"word-break: break-all;\"> The function f is defined by y = f(x) = 2 ln 4x, 0:01 <= x >= 1. <BR>\n" );
document.write( "c) Plot f from x = 0:01 to x = 1 and then plot f^(-1) on the same axes but only for domain values of x given by the range of f.<BR>\n" );
document.write( "-----------------------------------------------<BR>\n" );
document.write( "Find the equation of f^-1(x)<BR>\n" );
document.write( "Start with y = 2ln(4x)<BR>\n" );
document.write( "x = 2ln(4y)<BR>\n" );
document.write( "ln(4y) = x/2<BR>\n" );
document.write( "4y = e^(x/2)<BR>\n" );
document.write( "y = (1/4)e^(x/2)<BR>\n" );
document.write( "------------------------<BR>\n" );
document.write( "Graph y = 2ln(4x) and (1/4)e^(x/2)<BR>\n" );
document.write( "-----<BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=graph%28400%2C300%2C-10%2C10%2C-10%2C10%2C2%2Aln%284x%29%2C%281%2F4%292.71828%5E%28x%2F2%29%29 ALIGN=MIDDLE   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "-------------------------<BR>\n" );
document.write( "You will have to pick the segment of f(x) where 0.01<x<1<BR>\n" );
document.write( "and the segment of f^-1(x) that has the range of f as <BR>\n" );
document.write( "its domain.<BR>\n" );
document.write( "=========================================================<BR>\n" );
document.write( "Notice that the two curves are symmetric to the line y = x.<BR>\n" );
document.write( "Cheers,<BR>\n" );
document.write( "Stan H.  </SPAN>\n" );
document.write( "</TD></TR></TABLE>\n" );