Which of the following functions from Z into Z are bijections?

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KollegeApply · Accepted Answer

f(x) = x + 2 Explanation: For bijection on Z, f(x) must be one-one and onto Function f(x) = x2 + 1 is many-one as f(1) = f(–1) Range of f(x) = x3 is not Z for x ∈ Z. Also f(x) = 2x + 1 takes only values of types = 2k + 1 for x = k ∈ Z But f(x) = x + 2 takes all integral values for x ∈ Z Hence f(x)= x + 2 is bijection on Z

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