Let the function g : Z → Z be defined by g(x) = 7x + 3. (i) Show that g is one-to-one. (ii) Show that g is not onto.
The Answer to the Question
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Here's the Solution to this Question
is one-to-one iff
Show it must be true that
Therefore is one-to-one.
ONTO: Given any can we find an such that
But is not an integer. Hence there is no integer for and so is not onto.