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)}
f(x) = ax + b
(1, 1) ∈ f
⇒ f(1) = 1
⇒ a x 1 + b = 1
⇒ a + b = 1
(0, -1) ∈ f
⇒ f(0) = -1
⇒ a x 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.