Question

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.

Answer 1

f = {(1, 1), (2, 3), (0, –1), (–1, –3)} and f(x) = ax + b
(1, 1) ∈ f ⇒ f(1) = 1 ⇒ a × 1 + b = 1
⇒ a + b = 1
(0, –1) ∈ f ⇒ f(0) = –1 ⇒ a × 0 + b = –1
⇒ b = –1
On substituting b = –1 in a + b = 1,
We obtain a + (–1) = 1 ⇒ a = 1 + 1 = 2. Thus, the respective values of a and b are 2 and –1.