(a) What does it mean for a function to be injective (1-1)?
(b) What does it mean for a function to be surjective (onto)?
(c) Give an example of a function on the integers that is 1-1 but not onto.
(d) Give an example of a function on the integers that is onto but not 1-1.
a) an injective function or injection or one-to-one function is a function that preserves distinctness: it never maps distinct elements of its domain to the same element of its codomain.
b) The function f : R → R defined by f(x) = 2x + 1 is injective.
c) A surjective function is a function whose image is equal to its codomain. Equivalently, a function f with domainX and codomain Y is surjective if for every y in Y there exists at least one x in X with
d) The function f : R → R defined by f(x) = 2x + 1 is surjective (and even bijective), because for every real numbery we have an x such that f(x) = y: an appropriate x is (y − 1)/2.
Apr 21st, 2015
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