document.write( "<A HREF=/cgi-bin/jump-to-question.mpl?question=1096389>Question 1096389</A>: <I><SPAN STYLE=\"word-break: break-all;\"> Let f(x) = (x-2)^3+8\r<BR>\n" );
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document.write( "a. Show that this function is one-to-one algebraically.<BR>\n" );
document.write( "b. Find the inverse of f(x). </SPAN>\n" );
document.write( "</I><HR><TABLE width=100%><TR><TD><B><A HREF=http://www.algebra.com/>Algebra.Com's</A> Answer #710808 by </B><A HREF=/tutors/aboutme.mpl?userid=htmentor><B>htmentor(1343)</B></A><img src=\"/images/stars/stars-12.gif\" alt=\"\" >&nbsp;<A HREF=/tutors/aboutme.mpl?userid=htmentor><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=htmentor><BR>You can <A HREF=\"/cgi-bin/embed-solution.mpl?show=1&solution=710808\">put this solution on YOUR website!</A><BR><SPAN STYLE=\"word-break: break-all;\"> a. The function is one-to-one if we let f(a) = f(b) and are able to show that a = b.<BR>\n" );
document.write( "f(a) = (a-2)^3 + 8<BR>\n" );
document.write( "f(b) = (b-2)^2 + 8<BR>\n" );
document.write( "f(a) = f(b): (a-2)^3 + 8 = (b-2)^2 + 8<BR>\n" );
document.write( "(a-2)^3 = (b-2)^3<BR>\n" );
document.write( "Let A = a-2, B = b-2<BR>\n" );
document.write( "If A^3 = B^3 -> A = B, and therefore a = b<BR>\n" );
document.write( "b. To find the inverse of f(x) = y = (x-2)^3+8, replace x with y and solve for y:<BR>\n" );
document.write( "x = (y-2)^3 + 8 <BR>\n" );
document.write( "y-2 = (x-8)^(1/3)<BR>\n" );
document.write( "y = (x-8)^(1/3) + 2<BR>\n" );
document.write( "The inverse is f_inv(x) = (x-8)^(1/3) + 2<BR>\n" );
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