document.write( "<A HREF=/cgi-bin/jump-to-question.mpl?question=1163140>Question 1163140</A>: <I><SPAN STYLE=\"word-break: break-all;\"> How do i find the inverse function of: f(x)=ln√(e^x - 2)\r<BR>\n" );
document.write( "\n" );
document.write( "I started it like this:\r<BR>\n" );
document.write( "\n" );
document.write( "f(x)=y <=> y=ln√(e^x-2) <=> e^y = √(e^x-2) <=> e^2y = e^x - 2 <=> e^x = e^2y+2 <=> ???\r<BR>\n" );
document.write( "\n" );
document.write( "But I couldn't solve it till the end so i would appreciate any kind of help! </SPAN>\n" );
document.write( "</I><HR><TABLE width=100%><TR><TD><B><A HREF=http://www.algebra.com/>Algebra.Com's</A> Answer #787138 by </B><A HREF=/tutors/aboutme.mpl?userid=greenestamps><B>greenestamps(13200)</B></A><img src=\"/images/stars/stars-13.gif\" alt=\"\" >&nbsp;<A HREF=/tutors/aboutme.mpl?userid=greenestamps><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=greenestamps><BR>You can <A HREF=\"/cgi-bin/embed-solution.mpl?show=1&solution=787138\">put this solution on YOUR website!</A><BR><SPAN STYLE=\"word-break: break-all;\"> <br><BR>\n" );
document.write( "The answer from the other tutor demonstrates the standard way of finding the inverse of a function, which you were trying to do.<br><BR>\n" );
document.write( "For many functions, it is easy to find an inverse by using the idea that an inverse function \"un-does\" what the function does.<br><BR>\n" );
document.write( "Using that concept, the inverse function has to perform the opposite operations, and in the reverse order, compared to the original function.<br><BR>\n" );
document.write( "The given function does the following to the input value:<BR>\n" );
document.write( "(1) raise e to that power<BR>\n" );
document.write( "(2) subtract 2<BR>\n" );
document.write( "(3) take the square root<BR>\n" );
document.write( "(4) take the natural log<br><BR>\n" );
document.write( "The inverse function must then<BR>\n" );
document.write( "(1) raise e to the power<BR>\n" );
document.write( "(2) square it<BR>\n" );
document.write( "(3) add 2<BR>\n" );
document.write( "(4) take the natural log<br><BR>\n" );
document.write( "That sequence of operations gives us the inverse function:<br><BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=x ALIGN=MIDDLE  ALT=\"x\"   DISABLED_style= \"max-width:90%; height:auto;\" > --> <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=e%5Ex ALIGN=MIDDLE  ALT=\"e%5Ex\"   DISABLED_style= \"max-width:90%; height:auto;\" > --> <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=%28e%5Ex%29%5E2+=+e%5E%282x%29 ALIGN=MIDDLE  ALT=\"%28e%5Ex%29%5E2+=+e%5E%282x%29\"   DISABLED_style= \"max-width:90%; height:auto;\" > --> <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=e%5E%282x%29%2B2 ALIGN=MIDDLE  ALT=\"e%5E%282x%29%2B2\"   DISABLED_style= \"max-width:90%; height:auto;\" > --> <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=ln%28e%5E%282x%29%2B2%29 ALIGN=MIDDLE  ALT=\"ln%28e%5E%282x%29%2B2%29\"   DISABLED_style= \"max-width:90%; height:auto;\" ><br><BR>\n" );
document.write( " </SPAN>\n" );
document.write( "</TD></TR></TABLE>\n" );