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Misc 8 - Let f = {(1, 1), (2, 3), (0, -1), (-1, -3)}, f(x) = ax + b

Misc 8 - Chapter 2 Class 11 Relations and Functions - Part 2

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Misc 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. Given f(x) = ax + b i.e. y = ax + b Putting values of x and y in f(x) For (1, 1) y = ax + b 1 = a(1) + b 1 = a + b a + b = 1 For (2, 3) y = ax + b 3 = a(2) + b 3 = 2a + b 2a + b = 3 Calculating (2) – (1) 2a + b – (a + b) = 3 – 1 2a + b – a – b = 2 2a + b – a – b = 2 2a – a + b – b = 2 a + 0 = 2 a = 2 Putting a = 2 in (2) a + b = 1 2 + b = 1 b = 1 – 2 b = – 1 Hence, a = 2 & b = –1

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Davneet Singh has done his B.Tech from Indian Institute of Technology, Kanpur. He has been teaching from the past 13 years. He provides courses for Maths, Science, Social Science, Physics, Chemistry, Computer Science at Teachoo.