Question 643982
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Use the following intuitive definition of surjective to answer your questions.


A function f is surjective if it ‘hits’ everything in the target set; in your case the target set is Z, so a surjective function is one that ‘hits’ every integer. In less informal language this means that if n is any integer whatsoever, n=f(m) for at least one integer m.


In the case of all of your example functions, the target set is the set of all real numbers, *[tex \LARGE R].  So your "is this surjective?" question reduces to "are there any real numbers excluded from the range of the function?" and a "no" answer implies surjectivity.


John
*[tex \LARGE e^{i\pi}\ +\ 1\ =\ 0]
My calculator said it, I believe it, that settles it
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