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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.)
(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.
