(i) f : N → N : f(x) = x³ is one - one into.

f(x) = x³

Since the function f(x) is monotonically increasing from the domain N → N

∴f(x) is one –one

Range of f(x) = ( - ∞,∞)≠N(codomain)

∴f(x) is into

∴f : N → N : f(x) = x² is one - one into.

(ii) f : Z → Z : f(x) = x³ is one - one into

f(x) = x³

Since the function f(x) is monotonically increasing from the domain Z → Z

∴f(x) is one –one

Range of f(x) = ( - ∞,∞)≠Z(codomain)

∴f(x) is into

∴ f : Z → Z : f(x) = x³ is one - one into.