document.write( "<A HREF=/cgi-bin/jump-to-question.mpl?question=83566>Question 83566</A>This question is from textbook <A HREF=http://www.amazon.com/exec/obidos/ASIN/0618394664/algebrahomeworkh>PreCalculus - A Graphing Aproach</A><BR>\n" );
document.write( ": <I><SPAN STYLE=\"word-break: break-all;\"> The book asks for this group of problems to be tested to see if the function is one-to-one. The book gives an explanation of this test, but it is very short and of little help. Can you explain the testing process a little better? For instance, the example the book gives is f(x) = (sqrt x) + 1. It then assigns nonnegative real numbers a & b such that f(a) = f(b). In the end, a = b. How does this work with real problems like (3x+4)/5? </SPAN>\n" );
document.write( "</I><HR><TABLE width=100%><TR><TD><B><A HREF=http://www.algebra.com/>Algebra.Com's</A> Answer #60092 by </B><A HREF=/tutors/aboutme.mpl?userid=nilan><B>nilan(17)</B></A><img src=\"/images/stars/stars-06.gif\" alt=\"\" >&nbsp;<A HREF=/tutors/aboutme.mpl?userid=nilan><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=60092\">put this solution on YOUR website!</A><BR><SPAN STYLE=\"word-break: break-all;\"> The definition of one to one function says<BR>\n" );
document.write( "A function is said to be one to one if f(a)=f(b) then a=b\r<BR>\n" );
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document.write( "It means that no any deferent values map to one value<BR>\n" );
document.write( "So if you want to prove a given function is one to one, you have to do the general proof<BR>\n" );
document.write( "It means, getting arbitrary two values called a,b and suppose that f(a)=f(b) and show that finally a=b\r<BR>\n" );
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document.write( "It is enough to give a concrete example to show a given function is not one to one.\r<BR>\n" );
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document.write( "To show a function is one to one\r<BR>\n" );
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document.write( "F(x) = (3x+4)/5<BR>\n" );
document.write( "Let a and b are any real numbers and suppose<BR>\n" );
document.write( "f(a) =f(b)<BR>\n" );
document.write( "then<BR>\n" );
document.write( "(3a+4)/5 = (3b+4)/5<BR>\n" );
document.write( "3a+4=3b+4<BR>\n" );
document.write( "3a=3b<BR>\n" );
document.write( "a=b<BR>\n" );
document.write( "so f(x) is one to one\r<BR>\n" );
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document.write( "To show a function is not one to one <BR>\n" );
document.write( "f(x) = square(x)<BR>\n" );
document.write( " In the first site, we see that this is can’t be one to one since 1 and -1 map to 1<BR>\n" );
document.write( " So, in this case you can give this concrete example to how this is not one to one<BR>\n" );
document.write( "f(1)=f(-1) = 1<BR>\n" );
document.write( "Two deferent values map to a single value, hence this is not one to one. </SPAN>\n" );
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