document.write( "<A HREF=/cgi-bin/jump-to-question.mpl?question=166272>Question 166272</A>: <I><SPAN STYLE=\"word-break: break-all;\"> My problem is to find an inverse of the function f(x)=(3x+7)^3-5.  I know this is started as y=(3x+7)^3-5.  What steps follow and what is the answer?  Thanks for your help! </SPAN>\n" );
document.write( "</I><HR><TABLE width=100%><TR><TD><B><A HREF=http://www.algebra.com/>Algebra.Com's</A> Answer #122538 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=122538\">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=%283x%2B7%29%5E3-5 ALIGN=MIDDLE  ALT=\"y=%283x%2B7%29%5E3-5\"   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=%283y%2B7%29%5E3-5 ALIGN=MIDDLE  ALT=\"x=%283y%2B7%29%5E3-5\"   DISABLED_style= \"max-width:90%; height:auto;\" > Switch 'x' and 'y'. The goal now is to solve for 'y'\r<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=x%2B5=%283y%2B7%29%5E3 ALIGN=MIDDLE  ALT=\"x%2B5=%283y%2B7%29%5E3\"   DISABLED_style= \"max-width:90%; height:auto;\" > Add 5 to 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%2B5%29=3y%2B7 ALIGN=MIDDLE  ALT=\"root%283%2Cx%2B5%29=3y%2B7\"   DISABLED_style= \"max-width:90%; height:auto;\" > Take the cube root of both sides to eliminate the exponent of '3'\r<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=3y%2B7=root%283%2Cx%2B5%29 ALIGN=MIDDLE  ALT=\"3y%2B7=root%283%2Cx%2B5%29\"   DISABLED_style= \"max-width:90%; height:auto;\" > Rearrange the equation\r<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=3y=root%283%2Cx%2B5%29-7 ALIGN=MIDDLE  ALT=\"3y=root%283%2Cx%2B5%29-7\"   DISABLED_style= \"max-width:90%; height:auto;\" > Subtract 7 from both sides\r<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=y=%28root%283%2Cx%2B5%29-7%29%2F3 ALIGN=MIDDLE  ALT=\"y=%28root%283%2Cx%2B5%29-7%29%2F3\"   DISABLED_style= \"max-width:90%; height:auto;\" > Divide both sides by 3 to isolate (ie solve for) 'y'\r<BR>\n" );
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document.write( "So the inverse function is <IMG STYLE=\"max-width:80%;\" SRC=\"/cgi-bin/rendertex.cgi?\LARGE f^{-1}\left(x\right)=\frac{\sqrt[3]{x+5}-7}{3}\"> </SPAN>\n" );
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