document.write( "<A HREF=/cgi-bin/jump-to-question.mpl?question=1017935>Question 1017935</A>: <I><SPAN STYLE=\"word-break: break-all;\"> I am looking for the inverse function for f(x)= e^(2x).\r<BR>\n" );
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document.write( "I have found f^-1(x)=1/2 In(x), yet I can not find the others that also apply to this function and I am also unsure if f(x)=e^(2x) if the exponential function is its own inverse.\r<BR>\n" );
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document.write( "The choices are:<BR>\n" );
document.write( " 1. f^-1(x)= 1/e^(2x)\r<BR>\n" );
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document.write( " 2. f^-1(x) log_2(x)\r<BR>\n" );
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document.write( " 3.f^-1(x)= In&#8730;x\r<BR>\n" );
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document.write( " 4. f^-1(x)= In(x^2)\r<BR>\n" );
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document.write( "Please help me with this problem.<BR>\n" );
document.write( "Thank you. </SPAN>\n" );
document.write( "</I><HR><TABLE width=100%><TR><TD><B><A HREF=http://www.algebra.com/>Algebra.Com's</A> Answer #634154 by </B><A HREF=/tutors/aboutme.mpl?userid=richard1234><B>richard1234(7193)</B></A><img src=\"/images/stars/stars-13.gif\" alt=\"\" >&nbsp;<A HREF=/tutors/aboutme.mpl?userid=richard1234><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=richard1234><BR>You can <A HREF=\"/cgi-bin/embed-solution.mpl?show=1&solution=634154\">put this solution on YOUR website!</A><BR><SPAN STYLE=\"word-break: break-all;\"> If a function is one-to-one, it has a unique inverse function. The inverse of an expential function is a logarithmic function, so it cannot be itself.\r<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=\"/cgi-bin/rendertex.cgi?\large f^{-1}(x) = \frac{1}{2} \ln x\"> is correct. To check, you can simply compute <IMG STYLE=\"max-width:80%;\" SRC=\"/cgi-bin/rendertex.cgi?\large f^{-1}(f(x))\">\r<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=\"/cgi-bin/rendertex.cgi?\large f^{-1}(f(x)) = f^{-1}(e^{2x}) = \frac{1}{2} \ln (e^{2x}) = \frac{1}{2} \cdot 2x = x\">\r<BR>\n" );
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document.write( "Similarly, <IMG STYLE=\"max-width:80%;\" SRC=\"/cgi-bin/rendertex.cgi?\large f(f^{-1})(x) = x\">. So they are inverses. </SPAN>\n" );
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