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

InterviewSolution

1.

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

Answer»

Consider x₁, x₂ ∈ Z

We know that

f(x₁) = f(x₂)

So we get

x₁³ = x₂³

where x₁= 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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