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Ex 1.2, 7 - State whether one-one, onto or bijective - Class 12

Ex 1.2 , 7 - Chapter 1 Class 12 Relation and Functions - Part 2
Ex 1.2 , 7 - Chapter 1 Class 12 Relation and Functions - Part 3

 

 

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Ex 1.2 , 7 In each of the following cases, state whether the function is one-one, onto or bijective. Justify your answer. f: R → R defined by f(x) = 3 − 4x f(x) = 3 – 4x Checking one-one f (x1) = 3 – 4x1 f (x2) = 3 – 4x2 Putting f(x1) = f(x2) 3 – 4x1 = 3 – 4x2 Rough One-one Steps: 1. Calculate f(x1) 2. Calculate f(x2) 3. Putting f(x1) = f(x2) we have to prove x1 = x2 –4x1 = –4x2 x1 = x2. Hence, if f(x1) = f(x2) , Then x1 = x2 ∴ function f is one-one Onto f(x) = 3 − 4x Let f(x) = y , such that y ∈ R 3 – 4x = y –4x = y – 3 x = (𝑦 − 3)/(−4) Now, Checking for y = f(x) Putting value of x in f(x) f(x) = f((𝑦 − 3)/(−4)) = 3 − 4((𝑦 − 3)/(−4)) = 3 + (y − 3) = y Thus, for every y ∈ R, there exists x ∈ R such that f(x) = y Hence, f is onto

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Davneet Singh has done his B.Tech from Indian Institute of Technology, Kanpur. He has been teaching from the past 12 years. He provides courses for Maths, Science, Social Science, Physics, Chemistry, Computer Science at Teachoo.