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Ex 1.2

Ex 1.2, 1

Ex 1.2, 2 (i) Important

Ex 1.2, 2 (ii) Important

Ex 1.2, 2 (iii)

Ex 1.2, 2 (iv)

Ex 1.2, 2 (v) Important

Ex 1.2 , 3

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Ex 1.2, 5 Important

Ex 1.2 , 6 Important

Ex 1.2, 7 (i) You are here

Ex 1.2, 7 (ii)

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Ex 1.2 , 9

Ex 1.2 , 10 Important

Ex 1.2 , 11 (MCQ) Important

Ex 1.2, 12 (MCQ)

Last updated at June 5, 2023 by Teachoo

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