Question 8:
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
f = {(1, 1), (2, 3), (0, −1), (−1, −3)}
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.
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