document.write( "<A HREF=/cgi-bin/jump-to-question.mpl?question=1191974>Question 1191974</A>: <I><SPAN STYLE=\"word-break: break-all;\"> Let f(x) =2x-3 find f-1, ff-1(x), ff-1(4)  </SPAN>\n" );
document.write( "</I><HR><TABLE width=100%><TR><TD><B><A HREF=http://www.algebra.com/>Algebra.Com's</A> Answer #823888 by </B><A HREF=/tutors/aboutme.mpl?userid=greenestamps><B>greenestamps(13203)</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=823888\">put this solution on YOUR website!</A><BR><SPAN STYLE=\"word-break: break-all;\"> <br><BR>\n" );
document.write( "f(x)=2x-3<br><BR>\n" );
document.write( "(1) Find f^(-1)(x)<br><BR>\n" );
document.write( "There is a simple method for finding the inverse of a simple function like this, using the idea that an inverse function \"un-does\" what the function does.<br><BR>\n" );
document.write( "The given function does the following to the input:<BR>\n" );
document.write( ".. multiply by 2; and<BR>\n" );
document.write( ".. subtract 3<br><BR>\n" );
document.write( "The inverse function, to undo that the function does, must perform the opposite operations in the opposite order:<BR>\n" );
document.write( ".. add 3; and<BR>\n" );
document.write( ".. divide by 2<br><BR>\n" );
document.write( "ANSWER: f^(-1)(x) = (x+3)/2<br><BR>\n" );
document.write( "(2) By the definition of an inverse function, f(f^(-1)(x))=x<br><BR>\n" );
document.write( "(3) Likewise, f(f^(-1)(4))=4<br><BR>\n" );
document.write( " </SPAN>\n" );
document.write( "</TD></TR></TABLE>\n" );