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Show that the function  f: Z → Z: f(x) = x2 is many-one into.

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Consider A = {-1, 1, 2, 3} and B = {1, 4, 9}

It is given that f: A → B: f(x) = x2 Ɐ x ∈ A

Each element in A has unique image in B where f is a function from A to B

By substituting the values

f(-1) = (-1)2 = 1

f(1) = 12 = 1

f(2) = 22 = 4

f(3) = 32 = 9

Here, two elements -1 and 1 have same image 1 ∈ B

Hence, f is many-one.

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