document.write( "<A HREF=/cgi-bin/jump-to-question.mpl?question=51040>Question 51040</A>: <I><SPAN STYLE=\"word-break: break-all;\">     If f(x) = (x - 2)^1/3, then f^-1(x) =\r<BR>\n" );
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document.write( " a. (x3 + 1)/2<BR>\n" );
document.write( " b. (x3 - 1)/2<BR>\n" );
document.write( " c. (x3 + 2)/2<BR>\n" );
document.write( " d. (x3 - 2)/2<BR>\n" );
document.write( " e. x3 - 2<BR>\n" );
document.write( " f. x3 + 2<BR>\n" );
document.write( " g. none of these </SPAN>\n" );
document.write( "</I><HR><TABLE width=100%><TR><TD><B><A HREF=http://www.algebra.com/>Algebra.Com's</A> Answer #34017 by </B><A HREF=/tutors/aboutme.mpl?userid=Earlsdon><B>Earlsdon(6294)</B></A><img src=\"/images/stars/stars-13.gif\" alt=\"\" >&nbsp;<A HREF=/tutors/aboutme.mpl?userid=Earlsdon><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/images/nopicture.jpg><BR>You can <A HREF=\"/cgi-bin/embed-solution.mpl?show=1&solution=34017\">put this solution on YOUR website!</A><BR><SPAN STYLE=\"word-break: break-all;\"> If <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=f%28x%29+=+%28x-2%29%5E%281%2F3%29 ALIGN=MIDDLE  ALT=\"f%28x%29+=+%28x-2%29%5E%281%2F3%29\"   DISABLED_style= \"max-width:90%; height:auto;\" >, find <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=f%5E-1%28x%29 ALIGN=MIDDLE  ALT=\"f%5E-1%28x%29\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "First, replace f(x) with y, so now you have:<BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=y+=+%28x-2%29%5E%281%2F3%29 ALIGN=MIDDLE  ALT=\"y+=+%28x-2%29%5E%281%2F3%29\"   DISABLED_style= \"max-width:90%; height:auto;\" > Cube both sides.<BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=y%5E3+=+x-2 ALIGN=MIDDLE  ALT=\"y%5E3+=+x-2\"   DISABLED_style= \"max-width:90%; height:auto;\" > Interchange the variables.<BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=x%5E3+=+y-2 ALIGN=MIDDLE  ALT=\"x%5E3+=+y-2\"   DISABLED_style= \"max-width:90%; height:auto;\" > Now solve for y.<BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=y+=+x%5E3%2B2 ALIGN=MIDDLE  ALT=\"y+=+x%5E3%2B2\"   DISABLED_style= \"max-width:90%; height:auto;\" > Finally, replace y with <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=f%5E-1%28x%29 ALIGN=MIDDLE  ALT=\"f%5E-1%28x%29\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=f%5E-1%28x%29+=+x%5E3%2B2 ALIGN=MIDDLE  ALT=\"f%5E-1%28x%29+=+x%5E3%2B2\"   DISABLED_style= \"max-width:90%; height:auto;\" > This is choice f. in your list.\r<BR>\n" );
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document.write( "Check:<BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=f%28f%5E-1%28x%29%29+=+f%28x%5E3%2B2%29 ALIGN=MIDDLE  ALT=\"f%28f%5E-1%28x%29%29+=+f%28x%5E3%2B2%29\"   DISABLED_style= \"max-width:90%; height:auto;\" > = <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=%28%28x%5E3%2B2%29-2%29%5E%281%2F3%29+=+%28x%5E3%29%5E%281%2F3%29 ALIGN=MIDDLE  ALT=\"%28%28x%5E3%2B2%29-2%29%5E%281%2F3%29+=+%28x%5E3%29%5E%281%2F3%29\"   DISABLED_style= \"max-width:90%; height:auto;\" > = x<BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=f%5E-1%28f%28x%29%29+=+f%5E-1%28x-2%29%5E%281%2F3%29 ALIGN=MIDDLE  ALT=\"f%5E-1%28f%28x%29%29+=+f%5E-1%28x-2%29%5E%281%2F3%29\"   DISABLED_style= \"max-width:90%; height:auto;\" > = <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=%28%28x%5E3%2B2%29-2%29%5E%281%2F3%29+=+%28x%5E3%29%5E%281%2F3%29 ALIGN=MIDDLE  ALT=\"%28%28x%5E3%2B2%29-2%29%5E%281%2F3%29+=+%28x%5E3%29%5E%281%2F3%29\"   DISABLED_style= \"max-width:90%; height:auto;\" > = x\r<BR>\n" );
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document.write( "The above check is based on the following:<BR>\n" );
document.write( "f(x) and g(x) are inverses of each other iff:<BR>\n" );
document.write( "f(g(x)) = x for all x in the domain of g, and g(f(x)) = x for all x in the domain of f. </SPAN>\n" );
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