SOLUTION: Prove or disprove that h(x)=2x^3+1, where in h: integers (Z) → integers (Z) is a bijective function.

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Question 1167228: Prove or disprove that h(x)=2x^3+1, where in h: integers (Z) → integers (Z) is a bijective function.
Answer by ikleyn(52777) About Me  (Show Source):
You can put this solution on YOUR website!
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The map   x ---> 2x^3+1   from integer numbers to integer numbers is injective,  but is not bijective.


In other words,  the image of this map does not cover the entire set of integer numbers.


For example,  the number  11  does not belong to the image,  since the equation

            2x^3 + 1 = 11

has no solution in integer numbers (due to obvious reasons).