document.write( "<A HREF=/cgi-bin/jump-to-question.mpl?question=1165125>Question 1165125</A>: <I><SPAN STYLE=\"word-break: break-all;\"> g={(2,-1),(0,9),(1,-6),(2,-2)}<BR>\n" );
document.write( "h(x)=2x+9<BR>\n" );
document.write( "Find the following.<BR>\n" );
document.write( "g^-1(-2)=<BR>\n" );
document.write( "h^-1(x)=<BR>\n" );
document.write( "(h∘h^-1)(7)= </SPAN>\n" );
document.write( "</I><HR><TABLE width=100%><TR><TD><B><A HREF=http://www.algebra.com/>Algebra.Com's</A> Answer #789588 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=789588\">put this solution on YOUR website!</A><BR><SPAN STYLE=\"word-break: break-all;\"> <br><BR>\n" );
document.write( "(1) g^-1(-2) is the x value that produces a y value of -2.  From the given definition of g, that value is 2.<br><BR>\n" );
document.write( "(2) h^-1(x)...<br><BR>\n" );
document.write( "The formal algebraic approach: switch x and y and solve for the new y.<br><BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=y+=+2x%2B9 ALIGN=MIDDLE  ALT=\"y+=+2x%2B9\"   DISABLED_style= \"max-width:90%; height:auto;\" > --> <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=x+=+2y%2B9 ALIGN=MIDDLE  ALT=\"x+=+2y%2B9\"   DISABLED_style= \"max-width:90%; height:auto;\" ><br><BR>\n" );
document.write( "Solve for y:<br><BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=2y+=+x-9 ALIGN=MIDDLE  ALT=\"2y+=+x-9\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=y+=+%28x-9%29%2F2 ALIGN=MIDDLE  ALT=\"y+=+%28x-9%29%2F2\"   DISABLED_style= \"max-width:90%; height:auto;\" ><br><BR>\n" );
document.write( " A simple way to find the inverse of a function for many relatively simple functions....<br><BR>\n" );
document.write( "The function h(x) does this to the input: (1) multiply by 2; (2) add 9.<br><BR>\n" );
document.write( "The inverse function has to \"get you back where you started\".  To do that, it has to (1) subtract 9; (2) divide by 2.<br><BR>\n" );
document.write( "So the inverse function is <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=y+=+%28x-9%29%2F2 ALIGN=MIDDLE  ALT=\"y+=+%28x-9%29%2F2\"   DISABLED_style= \"max-width:90%; height:auto;\" ><br><BR>\n" );
document.write( "(3) By the definition of an inverse function, (h∘h^-1)(A)=A, so (h∘h^-1)(7)=7.<br><BR>\n" );
document.write( " </SPAN>\n" );
document.write( "</TD></TR></TABLE>\n" );