document.write( "<A HREF=/cgi-bin/jump-to-question.mpl?question=111761>Question 111761</A>This question is from textbook <A HREF=http://www.amazon.com/exec/obidos/ASIN/013311614x/algebrahomeworkh>College Algebra</A><BR>\n" );
document.write( ": <I><SPAN STYLE=\"word-break: break-all;\"> Hi I am stumbled with this problem:\r<BR>\n" );
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document.write( "Find the inverse function g of the given function, and state the domain and range of g.\r<BR>\n" );
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document.write( "y = f(x) = (x+2)^3\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 #81541 by </B><A HREF=/tutors/aboutme.mpl?userid=jim_thompson5910><B>jim_thompson5910(35256)</B></A><img src=\"/images/stars/stars-13.gif\" alt=\"\" >&nbsp;<A HREF=/tutors/aboutme.mpl?userid=jim_thompson5910><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=81541\">put this solution on YOUR website!</A><BR><SPAN STYLE=\"word-break: break-all;\"> <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=y=%28x%2B2%29%5E3 ALIGN=MIDDLE  ALT=\"y=%28x%2B2%29%5E3\"   DISABLED_style= \"max-width:90%; height:auto;\" > Start with the given equation\r<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=x=%28y%2B2%29%5E3 ALIGN=MIDDLE  ALT=\"x=%28y%2B2%29%5E3\"   DISABLED_style= \"max-width:90%; height:auto;\" > Switch x and y\r<BR>\n" );
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document.write( "Now let's solve for y\r<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=root%283%2Cx%29=y%2B2 ALIGN=MIDDLE  ALT=\"root%283%2Cx%29=y%2B2\"   DISABLED_style= \"max-width:90%; height:auto;\" > Take the cube root of both sides\r<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=root%283%2Cx%29-2=y ALIGN=MIDDLE  ALT=\"root%283%2Cx%29-2=y\"   DISABLED_style= \"max-width:90%; height:auto;\" > Subtract 2 from both sides\r<BR>\n" );
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document.write( "So our inverse function is <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=g%28x%29=root%283%2Cx%29-2 ALIGN=MIDDLE  ALT=\"g%28x%29=root%283%2Cx%29-2\"   DISABLED_style= \"max-width:90%; height:auto;\" >\r<BR>\n" );
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document.write( "Now if we graph, we get\r<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=+graph%28+500%2C+500%2C+-10%2C+10%2C+-10%2C+10%2C+x%5E%281%2F3%29-2%2C-%28-x%29%5E%281%2F3%29-2%29+ ALIGN=MIDDLE   DISABLED_style= \"max-width:90%; height:auto;\" > \r<BR>\n" );
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document.write( "So we can see that the domain and range of g is all real numbers (for both of them) </SPAN>\n" );
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