1. Chapter 1 Class 12 Relation and Functions
  2. Serial order wise
  3. Examples
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Question 1 - Examples - Chapter 1 Class 12 Relation and Functions

Last updated at Dec. 16, 2024 by Teachoo

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Question 1 Show that if f : R – {7/5} → R – {3/5} is defined by f(x) = (3𝑥 + 4)/(5𝑥 − 7) and g: R − {3/5}→ R – {7/5} is defined by g(x) = (7𝑥 + 4)/(5𝑥 − 3), then fog = IA and gof = IB, where A = R − {3/5} , B = R – {7/5} ; IA (x) = x, ∀ x ∈ A, IB (x) = x, ∀ x ∈ B are called identity functions on sets A and B, respectively. f(x) = (3𝑥 + 4)/(5𝑥 − 7) & g(x) = (7𝑥 + 4)/(5𝑥 − 3) Finding gof g(x) = (7𝑥 + 4)/(5𝑥 − 3) g(f(x)) = (7𝑓(𝑥) + 4)/(5𝑓(𝑥) − 3) gof = (7 ((3𝑥 + 4)/(5𝑥 − 7))" " + 4)/(5 (((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 − 28)/(15𝑥 + 20 − 15𝑥 + 21) = 41𝑥/41 = x Thus, gof = x = IB Finding fog f(x) = (3𝑥 + 4)/(5𝑥 − 7) f(g(x)) = (3𝑔(𝑥) + 4)/(5𝑔(𝑥) − 7) = (3 ((7𝑥 + 4)/(5𝑥 − 3)) + 4)/(5 (((7𝑥 + 4))/((5𝑥 − 3) )) − 7) = ((3(7𝑥 + 4) + 4(5𝑥 − 3))/(5𝑥 − 3))/((5(7𝑥 + 4) − 7(5𝑥 − 3))/(5𝑥 − 3)) = (3(7𝑥 + 4) + 4(5𝑥 − 3))/(5(7𝑥 + 4) − 7(5𝑥 − 3)) = (21𝑥 + 12 + 20𝑥 − 12)/(35𝑥 + 20 − 35𝑥 + 21) = 41𝑥/41 = x Thus, fog = x = IA Since fog = IA and gof = IB, Hence proved
  1. Chapter 1 Class 12 Relation and Functions
  2. Serial order wise

    3. Examples

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Chapter 1 Class 12 Relation and Functions
Serial order wise

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Davneet Singh

Davneet Singh has done his B.Tech from Indian Institute of Technology, Kanpur. He has been teaching from the past 14 years. He provides courses for Maths, Science and Computer Science at Teachoo