document.write( "<A HREF=/cgi-bin/jump-to-question.mpl?question=1090462>Question 1090462</A>: <I><SPAN STYLE=\"word-break: break-all;\"> If f(3)=1 and f(2x)=2f(x) for all x, find f^{-1}(64). </SPAN>\n" );
document.write( "</I><HR><TABLE width=100%><TR><TD><B><A HREF=http://www.algebra.com/>Algebra.Com's</A> Answer #704929 by </B><A HREF=/tutors/aboutme.mpl?userid=jim_thompson5910><B>jim_thompson5910(35256)</B></A><img src=\"/images/stars/stars-13.gif\" alt=\"\" >&nbsp;<A HREF=/tutors/aboutme.mpl?userid=jim_thompson5910><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=704929\">put this solution on YOUR website!</A><BR><SPAN STYLE=\"word-break: break-all;\"> <font color=\"black\" face=\"times\" size=\"3\"><BR>\n" );
document.write( "The goal is to use the definition f(2x) = 2*f(x) to build up to a case where f(x) = 64. If we know that x value, then we can find the inverse result. <BR>\n" );
document.write( "f(3) = 1<BR>\n" );
document.write( "-----------------<BR>\n" );
document.write( "f(2x) = 2*f(x)<BR>\n" );
document.write( "f(2*3) = 2*f(3) ... replace every x with 3<BR>\n" );
document.write( "f(6) = 2*1 ... replace f(3) with 1<BR>\n" );
document.write( "f(6) = 2<BR>\n" );
document.write( "-----------------<BR>\n" );
document.write( "f(2x) = 2*f(x)<BR>\n" );
document.write( "f(2*6) = 2*f(6) ... replace every x with 6<BR>\n" );
document.write( "f(12) = 2*2 ... replace f(6) with 2<BR>\n" );
document.write( "f(12) = 4<BR>\n" );
document.write( "-----------------<BR>\n" );
document.write( "f(2x) = 2*f(x)<BR>\n" );
document.write( "f(2*12) = 2*f(12) ... replace every x with 12<BR>\n" );
document.write( "f(24) = 2*4 ... replace f(12) with 4<BR>\n" );
document.write( "f(24) = 8<BR>\n" );
document.write( "-----------------<BR>\n" );
document.write( "f(2x) = 2*f(x)<BR>\n" );
document.write( "f(2*24) = 2*f(24) ... replace every x with 24<BR>\n" );
document.write( "f(48) = 2*8 ... replace f(24) with 8<BR>\n" );
document.write( "f(48) = 16<BR>\n" );
document.write( "-----------------<BR>\n" );
document.write( "f(2x) = 2*f(x)<BR>\n" );
document.write( "f(2*48) = 2*f(48) ... replace every x with 48<BR>\n" );
document.write( "f(96) = 2*16 ... replace f(48) with 16<BR>\n" );
document.write( "f(96) = 32<BR>\n" );
document.write( "-----------------<BR>\n" );
document.write( "f(2x) = 2*f(x)<BR>\n" );
document.write( "f(2*96) = 2*f(96) ... replace every x with 96<BR>\n" );
document.write( "f(192) = 2*32 ... replace f(96) with 32<BR>\n" );
document.write( "f(192) = 64<BR>\n" );
document.write( "-----------------<BR>\n" );
document.write( "Now we can apply the inverse<BR>\n" );
document.write( "f(192) = 64<BR>\n" );
document.write( "f^{-1}[ f(192) ] = f^{-1}[ 64 ]<BR>\n" );
document.write( "192 = f^{-1}[ 64 ]<BR>\n" );
document.write( "f^{-1}[ 64 ] = <font color=red size=4>192</font><BR>\n" );
document.write( "</font> </SPAN>\n" );
document.write( "</TD></TR></TABLE>\n" );