Let f = {(1, 1), (2, 3), (0, –1), (–1, –3)} be a linear function from Z into Z. Find f(x).

2x – 1 2x + 1 2x – 2 None of these

2x – 1

The correct answer is Option (1) → 2x – 1 Since f is a linear function, f(x) = mx + c. Also, since (1, 1), (0, – 1) ∈ R, f(1) = m + c = 1 and f(0) = c = –1. This gives m = 2 and f(x) = 2x – 1.