document.write( "<A HREF=/cgi-bin/jump-to-question.mpl?question=1007540>Question 1007540</A>: <I><SPAN STYLE=\"word-break: break-all;\"> Given the function f(x)= sqrt (7-5x)<BR>\n" );
document.write( "a. find the inverse f^-1(x)<BR>\n" );
document.write( "b. Determine  (F o 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 #623421 by </B><A HREF=/tutors/aboutme.mpl?userid=fractalier><B>fractalier(6550)</B></A><img src=\"/images/stars/stars-13.gif\" alt=\"\" >&nbsp;<A HREF=/tutors/aboutme.mpl?userid=fractalier><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=fractalier><BR>You can <A HREF=\"/cgi-bin/embed-solution.mpl?show=1&solution=623421\">put this solution on YOUR website!</A><BR><SPAN STYLE=\"word-break: break-all;\"> Given f(x)= sqrt(7-5x), we first plug y in for f(x), then switch x for y, and then solve for y...when we get that, we exchange f^-1(x) for y...like this...<BR>\n" );
document.write( "y = sqrt(7-5x)<BR>\n" );
document.write( "x = sqrt(7-5y)<BR>\n" );
document.write( "x^2 = 7 - 5y<BR>\n" );
document.write( "5y = 7 - x^2<BR>\n" );
document.write( "y = (1/5)(7 - x^2)<BR>\n" );
document.write( "f^-1(x) = (1/5)(7 - x^2)\r<BR>\n" );
document.write( "\n" );
document.write( "To answer b, remember that a function applied on its inverse or vice-versa has to yield x.  Thus<BR>\n" );
document.write( "(f o f^-1)(x) = x </SPAN>\n" );
document.write( "</TD></TR></TABLE>\n" );