document.write( "<A HREF=/cgi-bin/jump-to-question.mpl?question=1155728>Question 1155728</A>: <I><SPAN STYLE=\"word-break: break-all;\"> If f(x) = x+5/ 2 , then f-1(x) =  </SPAN>\n" );
document.write( "</I><HR><TABLE width=100%><TR><TD><B><A HREF=http://www.algebra.com/>Algebra.Com's</A> Answer #778371 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=778371\">put this solution on YOUR website!</A><BR><SPAN STYLE=\"word-break: break-all;\"> <br><BR>\n" );
document.write( "The function \"f(x) = x+5/2\" = <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=f%28x%29+=+x%2B5%2F2 ALIGN=MIDDLE  ALT=\"f%28x%29+=+x%2B5%2F2\"   DISABLED_style= \"max-width:90%; height:auto;\" > is not very interesting; so I am going to assume that the function is supposed to be \"f(x) = (x+5)/2\" = <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=f%28x%29+=+%28x%2B5%29%2F2 ALIGN=MIDDLE  ALT=\"f%28x%29+=+%28x%2B5%29%2F2\"   DISABLED_style= \"max-width:90%; height:auto;\" ><br><BR>\n" );
document.write( "The standard method for finding the inverse of a function is to switch the x and y in the given function and solve for the new y:<br><BR>\n" );
document.write( "Switch:  <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=y+=+%28x%2B5%29%2F2 ALIGN=MIDDLE  ALT=\"y+=+%28x%2B5%29%2F2\"   DISABLED_style= \"max-width:90%; height:auto;\" >  -->  <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=x+=+%28y%2B5%29%2F2 ALIGN=MIDDLE  ALT=\"x+=+%28y%2B5%29%2F2\"   DISABLED_style= \"max-width:90%; height:auto;\" ><br><BR>\n" );
document.write( "Now solve for y.<br><BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=x+=+%28y%2B5%29%2F2 ALIGN=MIDDLE  ALT=\"x+=+%28y%2B5%29%2F2\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=2x+=+y%2B5 ALIGN=MIDDLE  ALT=\"2x+=+y%2B5\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=2x-5+=+y ALIGN=MIDDLE  ALT=\"2x-5+=+y\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=y+=+2x-5 ALIGN=MIDDLE  ALT=\"y+=+2x-5\"   DISABLED_style= \"max-width:90%; height:auto;\" ><br><BR>\n" );
document.write( "ANSWER: f^(-1)(x) = 2x-5<br><BR>\n" );
document.write( "For many simple functions, it is easier to find the inverse by using the fact that the inverse function \"gets you back where you started\".<br><BR>\n" );
document.write( "To get you back where you started, the inverse function has to performs the opposite operations, in the opposite 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) add 5;<BR>\n" );
document.write( "(2) divide by 2<br><BR>\n" );
document.write( "The inverse function has to...<BR>\n" );
document.write( "(1) multiply by 2;<BR>\n" );
document.write( "(2) subtract 5<br><BR>\n" );
document.write( "f^(-1)(x) = 2x-5<br><BR>\n" );
document.write( "Same answer with much less work...<br><BR>\n" );
document.write( " </SPAN>\n" );
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