document.write( "<A HREF=/cgi-bin/jump-to-question.mpl?question=1200807>Question 1200807</A>: <I><SPAN STYLE=\"word-break: break-all;\"> Given that y=(r^3-8)^4/5, how do I find?\r<BR>\n" );
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document.write( "a. Inverse<BR>\n" );
document.write( "b. Any six (6) possible values that will be included in the domain of the above<BR>\n" );
document.write( "function </SPAN>\n" );
document.write( "</I><HR><TABLE width=100%><TR><TD><B><A HREF=http://www.algebra.com/>Algebra.Com's</A> Answer #835019 by </B><A HREF=/tutors/aboutme.mpl?userid=Theo><B>Theo(13342)</B></A><img src=\"/images/stars/stars-13.gif\" alt=\"\" >&nbsp;<A HREF=/tutors/aboutme.mpl?userid=Theo><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=Theo><BR>You can <A HREF=\"/cgi-bin/embed-solution.mpl?show=1&solution=835019\">put this solution on YOUR website!</A><BR><SPAN STYLE=\"word-break: break-all;\"> your equation is y = (r^3 - 8) ^ (4/5)<BR>\n" );
document.write( "let y = r and r = y to get:<BR>\n" );
document.write( "r = (y^3 - 8) ^ (4/5)<BR>\n" );
document.write( "raise both sides of this equation by the 5/4 power to get:<BR>\n" );
document.write( "r^(5/4) = y^3 - 8<BR>\n" );
document.write( "add 8 to both sides of the equation to get:<BR>\n" );
document.write( "r^( 5/4) + 8 = y^3<BR>\n" );
document.write( "raise both sides of the equation to the  1/3 power to get:<BR>\n" );
document.write( "(r^(5/4) + 8) ^ (1/3) = y<BR>\n" );
document.write( "that's your inverse equation.<BR>\n" );
document.write( "to graph this equation, let x = r to get:<BR>\n" );
document.write( "(x^(5/4) + 8) ^ (1/3) = y<BR>\n" );
document.write( "the graph looks like this.<BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" src = \"http://theo.x10hosting.com/2023/030804.jpg\"><BR>\n" );
document.write( "it is showing 2 equations.<BR>\n" );
document.write( "the first equation is y = (x^3 - 8) ^ (4/5)<BR>\n" );
document.write( "the second equation, which is the inverse euaation is y = (x^(5/4) + 8) ^ (1/3)<BR>\n" );
document.write( "the only difference between the graphed equations and the original equations is the x is used in place of r.<BR>\n" );
document.write( "your 6 possible values in the domain are x = 100, 200, 300, 400, 500, 600.<BR>\n" );
document.write( "as you can see fromk the graph, they will generate corresponding y values where (x,y) = (y,x).<BR>\n" );
document.write( "for example, the corresponding value for the point (12.157,400) in the original equation, will generate (400,12.157) in the inverse equation.<BR>\n" );
document.write( "note that only the positive side of the original equation generates a corresponding inverse equation.<BR>\n" );
document.write( "the negative side of the original equation will not generate an inverse because the fourth root of a number cannot be negative.<BR>\n" );
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