document.write( "<A HREF=/cgi-bin/jump-to-question.mpl?question=1039320>Question 1039320</A>: <I><SPAN STYLE=\"word-break: break-all;\"> Find the inverse function of f. <BR>\n" );
document.write( "f(x)= x^3 - 2  </SPAN>\n" );
document.write( "</I><HR><TABLE width=100%><TR><TD><B><A HREF=http://www.algebra.com/>Algebra.Com's</A> Answer #654056 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=654056\">put this solution on YOUR website!</A><BR><SPAN STYLE=\"word-break: break-all;\"> set y = f(x)<BR>\n" );
document.write( "equation becomes y = x^3 - 2<BR>\n" );
document.write( "replace y with x and x with y and the equation becomes x = y^3 - 2<BR>\n" );
document.write( "that is the inverse equation.<BR>\n" );
document.write( "you can solve it for x or you can leave it as is, and graph it.<BR>\n" );
document.write( "some software allows you to graph it as is.<BR>\n" );
document.write( "other software requires you to solve it for y.<BR>\n" );
document.write( "you can also graph it manually but that's labor intensive.<BR>\n" );
document.write( "i graphed it both ways (as is) and after solving for y just to show you it's the same graph.<BR>\n" );
document.write( "i also graphed the original equation and y = x.<BR>\n" );
document.write( "if it is the inverse equation, then it will be a reflection o the original equation about the line y = x.<BR>\n" );
document.write( "i also graphed the line y = -x + 8.<BR>\n" );
document.write( "this line is perpendicular to the line y = x and shows two selected points, one on the original equation and one on the inverse equation, that show they are reflections about the line y = x because (x,y) on the original equation is equal to (y,x) on the inverse equation.<BR>\n" );
document.write( "check out the graph to see what i mean.<BR>\n" );
document.write( "the equations in blue are the inverse equations.<BR>\n" );
document.write( "the original equation is red.<BR>\n" );
document.write( "(x+2)^(1/3) is the same as the cube root of (x+2).<BR>\n" );
document.write( "solving for y, start with x = y^3 - 2<BR>\n" );
document.write( "add 2 to both sides of the equation to get x+2 = y^3<BR>\n" );
document.write( "take the cube root of both sides of the equation to get y = cube root of (x+2).<BR>\n" );
document.write( "here's the graph.<BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" src = \"http://theo.x10hosting.com/2016/062601.jpg\" alt=\"$$$\" </><BR>\n" );
document.write( " </SPAN>\n" );
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