document.write( "<A HREF=/cgi-bin/jump-to-question.mpl?question=1040557>Question 1040557</A>: <I><SPAN STYLE=\"word-break: break-all;\"> Is | x | a one to one function?<BR>\n" );
document.write( "Is &#8730;x a one to one function?<BR>\n" );
document.write( "Is x^2 a one to one function? </SPAN>\n" );
document.write( "</I><HR><TABLE width=100%><TR><TD><B><A HREF=http://www.algebra.com/>Algebra.Com's</A> Answer #655407 by </B><A HREF=/tutors/aboutme.mpl?userid=ikleyn><B>ikleyn(52869)</B></A><img src=\"/images/stars/stars-13.gif\" alt=\"\" >&nbsp;<A HREF=/tutors/aboutme.mpl?userid=ikleyn><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=ikleyn><BR>You can <A HREF=\"/cgi-bin/embed-solution.mpl?show=1&solution=655407\">put this solution on YOUR website!</A><BR><SPAN STYLE=\"word-break: break-all;\"> .<BR>\n" );
document.write( "Is | x | a one to one function?<BR>\n" );
document.write( "Is &#8730;x a one to one function?<BR>\n" );
document.write( "Is x^2 a one to one function?<BR>\n" );
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document.write( "A function f with domain A is called a one-to-one function if every f(x)-value in the range B comes from only one x-value in A. <BR>\n" );
document.write( "(i.e. Every element in A is mapped/connected to a unique element in B.) \r<BR>\n" );
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document.write( "&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;(<A  rel=nofollow HREF=http://www.math.toronto.edu/preparing-for-calculus/4_functions/we_3_one_to_one.html>http://www.math.toronto.edu/preparing-for-calculus/4_functions/we_3_one_to_one.html</A>)\r<BR>\n" );
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document.write( "Is &nbsp;| x | &nbsp;a one to one function?          - No.\r\n" );
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document.write( "Is &nbsp;sqrt(x)&nbsp; a one to one function?        - Yes (in its domain and if you constrict the values of sqrt(x) by only positive real numbers).\r\n" );
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document.write( "Is &nbsp;x^2&nbsp; a one to one function?            - No\r\n" );
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document.write( "<U>comment from student</U>: Thank you!! However I forgot that the last equation should be x^2 - 1, is it still a one to one function?\r<BR>\n" );
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document.write( "<U>My response</U>\r<BR>\n" );
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document.write( "Is &nbsp;x^2-1&nbsp; a one to one function?          - No.  Same as x^2.\r\n" );
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