document.write( "<A HREF=/cgi-bin/jump-to-question.mpl?question=1169998>Question 1169998</A>: <I><SPAN STYLE=\"word-break: break-all;\"> The problem I got incorrect: <BR>\n" );
document.write( "Find inverse of h(x)=(3/4)x+12<BR>\n" );
document.write( "My steps...<BR>\n" );
document.write( "1) y = (3/4)x+12<BR>\n" );
document.write( "2) (4/3)y = x+12<BR>\n" );
document.write( "3) (4/3)y-12 = x<BR>\n" );
document.write( "4) (4/3)x-12 = y <BR>\n" );
document.write( "5) h^-1(x) = (4/3)x-12\r<BR>\n" );
document.write( "\n" );
document.write( "Am told correct answer should be h^-1(x) = (4/3)(x-12). <BR>\n" );
document.write( "Could someone explain the property I missed applying?  <BR>\n" );
document.write( "Thank you.  </SPAN>\n" );
document.write( "</I><HR><TABLE width=100%><TR><TD><B><A HREF=http://www.algebra.com/>Algebra.Com's</A> Answer #794892 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=794892\">put this solution on YOUR website!</A><BR><SPAN STYLE=\"word-break: break-all;\"> <br><BR>\n" );
document.write( "Between your steps (1) and (2), you attempted to multiply everything by 4/3, but you did not -- you didn't multiply the \"12\" by 4/3.  Your step (2) should show<br><BR>\n" );
document.write( "(4/3)y=x+16<br><BR>\n" );
document.write( "That would lead you to the answer<br><BR>\n" );
document.write( "h^-1(x) = (4/3)x-16<br><BR>\n" );
document.write( "which is equivalent to the given answer of<br><BR>\n" );
document.write( "h^-1(x) = (4/3)(x-12)<br><BR>\n" );
document.write( "------------------------------------<br><BR>\n" );
document.write( "Note for many simple functions, there is an easier and faster way to find the inverse of a function, using the idea that the inverse \"un-does\" what the function does.<br><BR>\n" );
document.write( "In this example, what the function does to the input is<BR>\n" );
document.write( "(1) multiply by (3/4); and<BR>\n" );
document.write( "(2) add 12<br><BR>\n" );
document.write( "To \"undo\" those operations, the inverse function has to perform the opposite operations in the opposite order:<BR>\n" );
document.write( "(1) subtract 12; and<BR>\n" );
document.write( "(2) divide by (3/4) -- i.e., multiply by (4/3)<br><BR>\n" );
document.write( "Those two steps immediately give you the inverse function:<br><BR>\n" );
document.write( "h^-1(x) = (4/3)(x-12)<br><BR>\n" );
document.write( "-----------------------------------------------<br><BR>\n" );
document.write( "comment from student....<br><BR>\n" );
document.write( "Thank you for suggestion on how to determine inverse of many simple functions; that appears a sound approach. But going back to my initial mistake, let’s consider only the part of this problem where we start with y isolated on one side ( y= (3/4)x+12 ), and we want to rearrange the equation so that instead x is the isolated variable. When I undo the multiplication of (3/4)x on the right side by dividing y on the left by 3/4 (actually multiplying by inverse), at that point, y is the only term on the left side. When proceeding by moving the 12 over to left I’m puzzled how I should have known to multiply it by 4/3 also (or that I could have stopped short of doing the final distribution by writing 4/3(x-12)). Is there something incorrect/unsound with beginning to rearrange the equation by undoing the multiplication? <br><BR>\n" );
document.write( "----------------------------------------------------<br><BR>\n" );
document.write( "No; there is nothing wrong with \"undoing the multiplication\" to start on the problem.  But you need to do it correctly.<br><BR>\n" );
document.write( "Undoing the multiplication means multiplying EVERYTHING on both sides of the equation by (4/3).  In your work, you only multiplied parts of the equation by (4/3).<br><BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=y+=+%283%2F4%29x%2B12 ALIGN=MIDDLE  ALT=\"y+=+%283%2F4%29x%2B12\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "--> <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=%284%2F3%29y+=+%284%2F3%29%283%2F4%29x+%2B+%284%2F3%2912 ALIGN=MIDDLE  ALT=\"%284%2F3%29y+=+%284%2F3%29%283%2F4%29x+%2B+%284%2F3%2912\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "--> <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=%284%2F3%29y+=+x+%2B+16 ALIGN=MIDDLE  ALT=\"%284%2F3%29y+=+x+%2B+16\"   DISABLED_style= \"max-width:90%; height:auto;\" ><br><BR>\n" );
document.write( "When you \"proceed\" from there, there is no \"12\" to move to the left; it is a \"16\". </SPAN>\n" );
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