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Show that the function f: Z → Z: f(x) = x3 is one-one and into.

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Consider x1, x2 ∈ Z

We know that

f(x1) = f(x2)

So we get

x13 = x23

where x= x2

Hence, f is one-one

Consider 2 ∈ Z, there exists no x ∈ Z where x3 = 2

Here, 2 ∈ Z has no pre-image in Z

Hence, f is into.

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