document.write( "<A HREF=/cgi-bin/jump-to-question.mpl?question=894815>Question 894815</A>: <I><SPAN STYLE=\"word-break: break-all;\"> Inverse Functions.\r<BR>\n" );
document.write( "\n" );
document.write( "1)Explain how to find the inverse of a function when the function is given in each of the following formats.\r<BR>\n" );
document.write( "\n" );
document.write( "a)As a table of inputs and outputs.\r<BR>\n" );
document.write( "\n" );
document.write( "b)As a graph.\r<BR>\n" );
document.write( "\n" );
document.write( "c)As a equation.\r<BR>\n" );
document.write( "<BR>\n" );
document.write( "<BR>\n" );
document.write( "\n" );
document.write( "2)Explain how to determine if two functions in equation form are inverses of each other and give a sample pair of functions for your classmates to practice determining if they are functions. </SPAN>\n" );
document.write( "</I><HR><TABLE width=100%><TR><TD><B><A HREF=http://www.algebra.com/>Algebra.Com's</A> Answer #542368 by </B><A HREF=/tutors/aboutme.mpl?userid=Theo><B>Theo(13342)</B></A><img src=\"/images/stars/stars-13.gif\" alt=\"\" >&nbsp;<A HREF=/tutors/aboutme.mpl?userid=Theo><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=Theo><BR>You can <A HREF=\"/cgi-bin/embed-solution.mpl?show=1&solution=542368\">put this solution on YOUR website!</A><BR><SPAN STYLE=\"word-break: break-all;\"> let's take a look at how we derive inverse functions by equation.\r<BR>\n" );
document.write( "<BR>\n" );
document.write( "\n" );
document.write( "if y = 5*x, then you find the inverse qeuation by replacing y with x and x with y and solving for y.\r<BR>\n" );
document.write( "<BR>\n" );
document.write( "\n" );
document.write( "y = 5*x becomes x = 5*y\r<BR>\n" );
document.write( "<BR>\n" );
document.write( "\n" );
document.write( "solve for y to get y = x/5.\r<BR>\n" );
document.write( "<BR>\n" );
document.write( "\n" );
document.write( "the inverse equation of y = 5x is y = x/5.\r<BR>\n" );
document.write( "<BR>\n" );
document.write( "\n" );
document.write( "that's by equation.\r<BR>\n" );
document.write( "<BR>\n" );
document.write( "\n" );
document.write( "now by table.\r<BR>\n" );
document.write( "<BR>\n" );
document.write( "\n" );
document.write( "take the same equation of y = 5x and make a table.\r<BR>\n" );
document.write( "<BR>\n" );
document.write( "\n" );
document.write( "you get:\r<BR>\n" );
document.write( "<BR>\n" );
document.write( "\n" );
document.write( "(x,y) = (1,5), (2,10), (3,15), (4,20), etc.\r<BR>\n" );
document.write( "<BR>\n" );
document.write( "\n" );
document.write( "now replace x with y and replace y with x to get:\r<BR>\n" );
document.write( "<BR>\n" );
document.write( "\n" );
document.write( "(x,y) = (5,1), (10,2), (15,3), (20,4), etc.\r<BR>\n" );
document.write( "<BR>\n" );
document.write( "\n" );
document.write( "the first table gets you the equation of y = 5x.\r<BR>\n" );
document.write( "<BR>\n" );
document.write( "\n" );
document.write( "the second table gets you the equation of y = x/5.\r<BR>\n" );
document.write( "<BR>\n" );
document.write( "\n" );
document.write( "all you do is interchange the x valuea and the y values and you have a table for the inverse equation.\r<BR>\n" );
document.write( "<BR>\n" );
document.write( "\n" );
document.write( "graphically, you would plot the (x,y) points for y = 5x.\r<BR>\n" );
document.write( "<BR>\n" );
document.write( "\n" );
document.write( "for each (x,y) point, you would plot the corresponding point of (y,x).\r<BR>\n" );
document.write( "<BR>\n" );
document.write( "\n" );
document.write( "if you then draw the line y = x on your graph you will see that the points of (y,x) are reflections of the points (x,y) about the line y = x.\r<BR>\n" );
document.write( "<BR>\n" );
document.write( "\n" );
document.write( "here's your graph.\r<BR>\n" );
document.write( "<BR>\n" );
document.write( "\n" );
document.write( "you find the reflected points about the line y = x by drawing a line vertical to that line (represented by y = -x) and then finding the intersection of that vertical line with the reflected lines of y = 5x and y = x/5.\r<BR>\n" );
document.write( "<BR>\n" );
document.write( "\n" );
document.write( "the point of intersection will be interchanged.\r<BR>\n" );
document.write( "<BR>\n" );
document.write( "\n" );
document.write( "(10,2) becomes (2,10) and (-10,-2) becomes (-2,-10) as seen on the graph.\r<BR>\n" );
document.write( "<BR>\n" );
document.write( "<BR>\n" );
document.write( "\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" src = \"http://theo.x10hosting.com/2014/082501.jpg\" alt=\"$$$\" </>\r<BR>\n" );
document.write( "<BR>\n" );
document.write( "\n" );
document.write( " </SPAN>\n" );
document.write( "</TD></TR></TABLE>\n" );