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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. |
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Answer» 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. |
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