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Consider the function f: N -> Z defined by f(x) = (-1)^(x-1). Determine its range.

1. (A) {-1, 1}
2. (B) [-1, 1]
3. (C) {0, 1}
4. (D) {0, 1, -1}

Correct answer: (A) {-1, 1}

Solution

For x in N: f(1) = (-1)⁰ = 1, f(2) = (-1)¹ = -1, f(3) = 1, f(4) = -1, alternating. The only outputs are +1 and -1, so the range is the discrete set {-1, 1}, not the interval [-1, 1].

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