# Example 17

Last updated at Dec. 8, 2016 by Teachoo

Last updated at Dec. 8, 2016 by Teachoo

Transcript

Example 17 Show that if f : R – 75 → R – 35 is defined by f(x) = 3𝑥 + 45𝑥 − 7 and g: R − 35→ R – 75 is defined by g(x) = 7𝑥 + 45𝑥 − 3, then fog = IA and gof = IB, where A = R − 35 , B = R – 75 ; IA (x) = x, ∀ x ∈ A, IB (x) = x, ∀ x ∈ B are called identity functions on sets A and B, respectively. f(x) = 3𝑥 + 45𝑥 − 7 & g(x) = 7𝑥 + 45𝑥 − 3 Finding gof g(x) = 7𝑥 + 45𝑥 − 3 g(f(x)) = 7𝑓(𝑥) + 45𝑓(𝑥) − 3 gof = 7 3𝑥 + 45𝑥 − 7 + 45 3𝑥 + 4 5𝑥 − 7 − 3 = 7 3𝑥 + 4 + 4(5𝑥 − 7)5𝑥 − 7 5 3𝑥 + 4 −3(5𝑥 − 7)5𝑥 − 7 = 7 3𝑥 + 4 + 4(5𝑥 − 7)5 3𝑥 + 4 −3(5𝑥 − 7) = 21𝑥 + 28 + 20𝑥 − 2815𝑥 + 20 − 15𝑥 + 21 = 41𝑥41 = x Thus, gof = x = IB Finding fog f(x) = 3𝑥 + 45𝑥 − 7 f(g(x)) = 3𝑔(𝑥) + 45𝑔(𝑥) − 7 = 3 7𝑥 + 45𝑥 − 3 + 45 7𝑥 + 4 5𝑥 − 3 − 3 = 3 7𝑥 + 4 + 4(5𝑥 − 3)5𝑥 − 3 5 7𝑥 + 4 − 3(5𝑥 − 3)5𝑥 − 3 = 3 7𝑥 + 4 + 4(5𝑥 − 3)5 7𝑥 + 4 − 3(5𝑥 − 3) = 21𝑥 + 12 + 20𝑥 − 1235𝑥 + 20 − 35𝑥 + 21 = 41𝑥41 = x Thus, fog = x = IA

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Chapter 1 Class 12 Relation and Functions

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About the Author

Davneet Singh

Davneet Singh is a graduate from Indian Institute of Technology, Kanpur. He has been teaching from the past 7 years. He provides courses for Mathematics and Science from Class 6 to 12. You can learn personally from here https://www.teachoo.com/premium/maths-and-science-classes/.