Let f = {(1, 1), (2, 3), (0, –1), (–1, –3)} be a function from Z to Z defined by f(x) = ax + b, for some integers a, b. Determine a, b.

Question

Philoid · Accepted Answer

Given: f = {(1, 1), (2, 3), (0, –1), (–1, –3)}

f(x) = ax + b

(1,1) Є f ⇒ for x = 1, f(x) = 1

⇒ 1 = a(1) + b

⇒ a+b = 1 …. (1)

Similarly, (0, -1) Є f ⇒ for x = 0, f(x) = -1

⇒ -1 = a(0) + b

⇒ b = -1

⇒ a-1 = 1 (from 1)

⇒ a = 2.

Hence a = 2 and b = -1.