document.write( "<A HREF=/cgi-bin/jump-to-question.mpl?question=209169>Question 209169</A>: <I><SPAN STYLE=\"word-break: break-all;\"> Hi all, Im having trouble with the following Function and Domain problem(s).<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).<BR>\n" );
document.write( "b) Write down the domain of f^(-1)<BR>\n" );
document.write( "Any help would be most appreciated.<BR>\n" );
document.write( "-Nick. </SPAN>\n" );
document.write( "</I><HR><TABLE width=100%><TR><TD><B><A HREF=http://www.algebra.com/>Algebra.Com's</A> Answer #158108 by </B><A HREF=/tutors/aboutme.mpl?userid=rapaljer><B>rapaljer(4671)</B></A><img src=\"/images/stars/stars-13.gif\" alt=\"\" >&nbsp;<A HREF=/tutors/aboutme.mpl?userid=rapaljer><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=rapaljer><BR>You can <A HREF=\"/cgi-bin/embed-solution.mpl?show=1&solution=158108\">put this solution on YOUR website!</A><BR><SPAN STYLE=\"word-break: break-all;\"> Hi Nick!!\r<BR>\n" );
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document.write( "Given <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=y=+2+ln%284x%29 ALIGN=MIDDLE  ALT=\"y=+2+ln%284x%29\"   DISABLED_style= \"max-width:90%; height:auto;\" >, you must solve for x by \"undoing\" all the operations that were done to it.  You must undo mult by 2, undo the \"ln\" function, and undo multiplication by 4.  That brings you down to x.\r<BR>\n" );
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document.write( "Start by dividing both sides by 2:<BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=y%2F2=+ln%284x%29 ALIGN=MIDDLE  ALT=\"y%2F2=+ln%284x%29\"   DISABLED_style= \"max-width:90%; height:auto;\" >\r<BR>\n" );
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document.write( "In order to \"undo\" the \"ln\", you must raise both sides as a power of e:\r<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=e%5E%28y%2F2%29+=+e%5E%28ln%284x%29%29+ ALIGN=MIDDLE  ALT=\"e%5E%28y%2F2%29+=+e%5E%28ln%284x%29%29+\"   DISABLED_style= \"max-width:90%; height:auto;\" >\r<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=e%5E%28y%2F2%29+=+4x+ ALIGN=MIDDLE  ALT=\"e%5E%28y%2F2%29+=+4x+\"   DISABLED_style= \"max-width:90%; height:auto;\" >\r<BR>\n" );
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document.write( "Last, divide both sides by 4:\r<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=%28e%5E%28y%2F2%29%29%2F4+=+x ALIGN=MIDDLE  ALT=\"%28e%5E%28y%2F2%29%29%2F4+=+x\"   DISABLED_style= \"max-width:90%; height:auto;\" >\r<BR>\n" );
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document.write( "In the above statements, y represents f(x).\r<BR>\n" );
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document.write( "NOW, if you interchange the x and the y, the NEW y represents the inverse function <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=f%5E-1%28x%29 ALIGN=MIDDLE  ALT=\"f%5E-1%28x%29\"   DISABLED_style= \"max-width:90%; height:auto;\" >.\r<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=y=%28e%5E%28y%2F2%29%29%2F4+=+f%5E-1%28x%29 ALIGN=MIDDLE  ALT=\"y=%28e%5E%28y%2F2%29%29%2F4+=+f%5E-1%28x%29\"   DISABLED_style= \"max-width:90%; height:auto;\" >\r<BR>\n" );
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document.write( "R^2\r<BR>\n" );
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document.write( "Dr. Robert J. Rapalje, Retired<BR>\n" );
document.write( "Seminole Community College<BR>\n" );
document.write( "Florida\r<BR>\n" );
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document.write( " </SPAN>\n" );
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