document.write( "<A HREF=/cgi-bin/jump-to-question.mpl?question=1097252>Question 1097252</A>: <I><SPAN STYLE=\"word-break: break-all;\"> Write an equation for the inverse of the given&#8203; one-to-one function.\r<BR>\n" );
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document.write( "f(x) = (5x+4)/(7) </SPAN>\n" );
document.write( "</I><HR><TABLE width=100%><TR><TD><B><A HREF=http://www.algebra.com/>Algebra.Com's</A> Answer #711649 by </B><A HREF=/tutors/aboutme.mpl?userid=greenestamps><B>greenestamps(13195)</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=711649\">put this solution on YOUR website!</A><BR><SPAN STYLE=\"word-break: break-all;\"> <br>The standard way I have seen taught for finding an inverse function is to switch the x and y variables and solve for the new y.<br><BR>\n" );
document.write( "That makes sense, because an inverse function is supposed to \"un-do\" what the function does.<br><BR>\n" );
document.write( "So let's do this.<br><BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=y+=+%285x%2B4%29%2F7 ALIGN=MIDDLE  ALT=\"y+=+%285x%2B4%29%2F7\"   DISABLED_style= \"max-width:90%; height:auto;\" >  -->  <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=x+=+%285y%2B4%29%2F7 ALIGN=MIDDLE  ALT=\"x+=+%285y%2B4%29%2F7\"   DISABLED_style= \"max-width:90%; height:auto;\" ><br><BR>\n" );
document.write( "Now solve the new equation for y.<br><BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=x+=+%285y%2B4%29%2F7 ALIGN=MIDDLE  ALT=\"x+=+%285y%2B4%29%2F7\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=7x+=+5y%2B4 ALIGN=MIDDLE  ALT=\"7x+=+5y%2B4\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=7x-4+=+5y ALIGN=MIDDLE  ALT=\"7x-4+=+5y\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=y+=+%287x-4%29%2F5 ALIGN=MIDDLE  ALT=\"y+=+%287x-4%29%2F5\"   DISABLED_style= \"max-width:90%; height:auto;\" ><br><BR>\n" );
document.write( "Now here is a faster way to reach the same answer without the formal algebra.  It will work for many relatively simple functions.<br><BR>\n" );
document.write( "Again, think about the fact that the inverse function is supposed to \"un-do\" what the function does.<br><BR>\n" );
document.write( "So look at the original function.  What does it \"do\" to x to get y?  It does these three things, in order:<BR>\n" );
document.write( "(1) multiply by 5<BR>\n" );
document.write( "(2) add 4<BR>\n" );
document.write( "(3) divide by 7<br><BR>\n" );
document.write( "To \"un-do\" what the function does, the inverse function should do the opposite operations, in the reverse order:<BR>\n" );
document.write( "(1) multiply by 7  (<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=x ALIGN=MIDDLE  ALT=\"x\"   DISABLED_style= \"max-width:90%; height:auto;\" > --> <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=7x ALIGN=MIDDLE  ALT=\"7x\"   DISABLED_style= \"max-width:90%; height:auto;\" >)<BR>\n" );
document.write( "(2) subtract 4  (<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=7x ALIGN=MIDDLE  ALT=\"7x\"   DISABLED_style= \"max-width:90%; height:auto;\" > --> <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=7x-4 ALIGN=MIDDLE  ALT=\"7x-4\"   DISABLED_style= \"max-width:90%; height:auto;\" >)<BR>\n" );
document.write( "(3) divide by 5  (<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=7x-4 ALIGN=MIDDLE  ALT=\"7x-4\"   DISABLED_style= \"max-width:90%; height:auto;\" > --> <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=%287x-4%29%2F5 ALIGN=MIDDLE  ALT=\"%287x-4%29%2F5\"   DISABLED_style= \"max-width:90%; height:auto;\" >)<br><BR>\n" );
document.write( "You can see that we get the same answer as with the formal algebra; not only that, but the steps are EXACTLY THE SAME as with the formal algebraic method.<br><BR>\n" );
document.write( "You might want to try this method the next time you need to find an inverse function, to see if the method \"works\" for you. </SPAN>\n" );
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