document.write( "<A HREF=/cgi-bin/jump-to-question.mpl?question=1179074>Question 1179074</A>: <I><SPAN STYLE=\"word-break: break-all;\"> Find the inverse of the one-to-one function.\r<BR>\n" );
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document.write( "f(x) = (x - 5)3\r<BR>\n" );
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document.write( "Group of answer choices\r<BR>\n" );
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document.write( "</I><HR><TABLE width=100%><TR><TD><B><A HREF=http://www.algebra.com/>Algebra.Com's</A> Answer #808579 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=808579\">put this solution on YOUR website!</A><BR><SPAN STYLE=\"word-break: break-all;\"> <br><BR>\n" );
document.write( "I suspect the given function is supposed to be <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=%28x-5%29%5E3 ALIGN=MIDDLE  ALT=\"%28x-5%29%5E3\"   DISABLED_style= \"max-width:90%; height:auto;\" > (\"(x-5)^3\") instead of <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=%28x-5%293 ALIGN=MIDDLE  ALT=\"%28x-5%293\"   DISABLED_style= \"max-width:90%; height:auto;\" > (\"(x-5)3\")...<br><BR>\n" );
document.write( "In typed text, it is standard to use \"^\" to denote exponentiation.<br><BR>\n" );
document.write( "The standard method for finding the inverse of a function is to switch the 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+=+%28x-5%29%5E3 ALIGN=MIDDLE  ALT=\"y+=+%28x-5%29%5E3\"   DISABLED_style= \"max-width:90%; height:auto;\" > --> <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=x+=+%28y-5%29%5E3 ALIGN=MIDDLE  ALT=\"x+=+%28y-5%29%5E3\"   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=x+=+%28y-5%29%5E3 ALIGN=MIDDLE  ALT=\"x+=+%28y-5%29%5E3\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=x%5E%281%2F3%29+=+y-5 ALIGN=MIDDLE  ALT=\"x%5E%281%2F3%29+=+y-5\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=y+=+x%5E%281%2F3%29%2B5 ALIGN=MIDDLE  ALT=\"y+=+x%5E%281%2F3%29%2B5\"   DISABLED_style= \"max-width:90%; height:auto;\" ><br><BR>\n" );
document.write( "ANSWER: the inverse function is <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=f%5E%28-1%29%28x%29+=+x%5E%281%2F3%29%2B5 ALIGN=MIDDLE  ALT=\"f%5E%28-1%29%28x%29+=+x%5E%281%2F3%29%2B5\"   DISABLED_style= \"max-width:90%; height:auto;\" ><br><BR>\n" );
document.write( "For a relatively simple function like this, the inverse function can be found much faster using the idea that the inverse function \"gets you back where you started\" by performing the inverse operations in the opposite order.  For this example, we have....<br><BR>\n" );
document.write( "The given function (a) subtracts 5 and (b) cubes the result<br><BR>\n" );
document.write( "The inverse function must (a) take the cube root and (b) add 5<br><BR>\n" );
document.write( "ANSWER: The inverse function is <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=x%5E%281%2F3%29%2B5 ALIGN=MIDDLE  ALT=\"x%5E%281%2F3%29%2B5\"   DISABLED_style= \"max-width:90%; height:auto;\" ><br><BR>\n" );
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