document.write( "<A HREF=/cgi-bin/jump-to-question.mpl?question=45520>Question 45520</A>This question is from textbook <A HREF=http://www.amazon.com/exec/obidos/ASIN/0534373526/algebrahomeworkh>College Algebra</A><BR>\n" );
document.write( ": <I><SPAN STYLE=\"word-break: break-all;\"> Use the property of Inverse Functions to show that f and g are inverses of each other:\r<BR>\n" );
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document.write( "f(x) = x^3 + 1; g(x) = (x-1)^(1/3)\r<BR>\n" );
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document.write( "f(g(x)) = f((x-1)^1/3) + 1 = x-1 + 1 = x<BR>\n" );
document.write( "g(f(x)) = g(x^3 + 1) = (x^3 + 1)^3 + 1 = x + 1 -1 = x\r<BR>\n" );
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document.write( "f and g are inverses of each other.\r<BR>\n" );
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document.write( "Thank you very much! </SPAN>\n" );
document.write( "</I><HR><TABLE width=100%><TR><TD><B><A HREF=http://www.algebra.com/>Algebra.Com's</A> Answer #30243 by </B><A HREF=/tutors/aboutme.mpl?userid=stanbon><B>stanbon(75887)</B></A><img src=\"/images/stars/stars-13.gif\" alt=\"\" >&nbsp;<A HREF=/tutors/aboutme.mpl?userid=stanbon><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=30243\">put this solution on YOUR website!</A><BR><SPAN STYLE=\"word-break: break-all;\"> f(x) = x^3 + 1; g(x) = (x-1)^(1/3) <BR>\n" );
document.write( "f(g(x)) = f((x-1)^1/3)^3 + 1 = x-1 + 1 = x<BR>\n" );
document.write( "g(f(x)=g(x^3 + 1) = [(x^3+1-1)^(1/3)]=[x^3]^(1/3) = x \r<BR>\n" );
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document.write( "Your conclusion is correct but I have adjusted your<BR>\n" );
document.write( "posting.\r<BR>\n" );
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document.write( "Cheers,<BR>\n" );
document.write( "Stan H. <BR>\n" );
document.write( " </SPAN>\n" );
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