Last updated at Jan. 28, 2020 by Teachoo

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Ex 2.3, 5 Find the range of each of the following functions. f(x) = 2 – 3x, x ∈ R, x > 0. Given that x > 0, Multiplying 3 both sides 3x > 0 × 3 3x > 0 Multiplying -1 both sides – 1 × 3x < – 1 × 0 – 3x < 0 Adding 2 both sides 2 – 3x < 2 + 0 (We need to make it in form 2 – 3x) 2 – 3x < 2 f(x) < 2 We note that value of f(x) is less than 2 (not including 2) Hence, Range = ( –∞, 2) Ex 2.3, 5 Find the range of each of the following functions. (ii) f(x) = x2 + 2, x, is a real number. We know that Square of a number will always be positive or 0 So we can say that x2 ≥ 0 Adding 2 both sides x2 + 2 ≥ 0 + 2 x2 + 2 ≥ 2 f(x) ≥ 2 ∴ Range of f = [2, ∞) (We need to make it of form x2 + 2) Ex 2.3, 5 Find the range of each of the following functions. (iii) f(x) = x, x is a real number Here we are given x is real We find values of f(x) by putting different values of x We can see that f(x) can be all real numbers as x is all real number ∴ Range of f(x) = R

About the Author

Davneet Singh

Davneet Singh is a graduate from Indian Institute of Technology, Kanpur. He has been teaching from the past 10 years. He provides courses for Maths and Science at Teachoo.