Question 1040557
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Is | x | a one to one function?
Is √x a one to one function?
Is x^2 a one to one function?
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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. 
(i.e. Every element in A is mapped/connected to a unique element in B.) 


&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;(<A 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>)


<pre>
Is &nbsp;| x | &nbsp;a one to one function?          - No.

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).

Is &nbsp;x^2&nbsp; a one to one function?            - No
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<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?


<U>My response</U>

<pre>
Is &nbsp;x^2-1&nbsp; a one to one function?          - No.  Same as x^2.
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