SOLUTION: 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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Question 1040557: Is | x | a one to one function?
Is √x a one to one function?
Is x^2 a one to one function?
Answer by ikleyn(52864)   (Show Source): You can put this solution on YOUR website!
.
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.)

      (http://www.math.toronto.edu/preparing-for-calculus/4_functions/we_3_one_to_one.html) 

Is  | x |  a one to one function?          - No.

Is  sqrt(x)  a one to one function?        - Yes (in its domain and if you constrict the values of sqrt(x) by only positive real numbers).

Is  x^2  a one to one function?            - No


comment from student: Thank you!! However I forgot that the last equation should be x^2 - 1, is it still a one to one function?

My response 
Is  x^2-1  a one to one function?          - No.  Same as x^2.


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