Answer :

Define f: N Z as f(x) = x and g: Z Z as g(x) = |x|

Now, we can see that


g(-1) = |-1| = 1


g(1) = |1| = 1


g(-1) = g(1) , but -1 ≠ 1


g is not injective.


Now, gof: N Z is defined as gof(x) = g(f(x)) = g(x) = |x|


Let x, y ϵ N such that gof(x) = gof(y).


|x| = |y|


x = y


Therefore, gof is injective.


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