Question 1 - Examples - Chapter 1 Class 12 Relation and Functions
Last updated at July 31, 2026 by Teachoo
Examples
Example 1
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Chapter 1 Class 12 Relation and Functions
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Question 1 Show that if f : R ā {7/5} ā R ā {3/5} is defined by f(x) = (3š„ + 4)/(5š„ ā 7) and g: R ā {3/5}ā R ā {7/5} is defined by g(x) = (7š„ + 4)/(5š„ ā 3), then fog = IA and gof = IB, where A = R ā {3/5} , B = R ā {7/5} ; IA (x) = x, ā x ā A, IB (x) = x, ā x ā B are called identity functions on sets A and B, respectively. f(x) = (3š„ + 4)/(5š„ ā 7) & g(x) = (7š„ + 4)/(5š„ ā 3) Finding gof g(x) = (7š„ + 4)/(5š„ ā 3) g(f(x)) = (7š(š„) + 4)/(5š(š„) ā 3) gof = (7 ((3š„ + 4)/(5š„ ā 7))" " + 4)/(5 (((3š„ + 4))/((5š„ ā 7) )) ā 3) = ((7(3š„ + 4) + 4(5š„ ā 7))/(5š„ ā 7))/((5(3š„ + 4) ā 3(5š„ ā 7))/(5š„ ā 7)) = (7(3š„ + 4) + 4(5š„ ā 7))/(5(3š„ + 4) ā 3(5š„ ā 7)) = (21š„ + 28 + 20š„ ā 28)/(15š„ + 20 ā 15š„ + 21) = 41š„/41 = x Thus, gof = x = IB Finding fog f(x) = (3š„ + 4)/(5š„ ā 7) f(g(x)) = (3š(š„) + 4)/(5š(š„) ā 7) = (3 ((7š„ + 4)/(5š„ ā 3)) + 4)/(5 (((7š„ + 4))/((5š„ ā 3) )) ā 7) = ((3(7š„ + 4) + 4(5š„ ā 3))/(5š„ ā 3))/((5(7š„ + 4) ā 7(5š„ ā 3))/(5š„ ā 3)) = (3(7š„ + 4) + 4(5š„ ā 3))/(5(7š„ + 4) ā 7(5š„ ā 3)) = (21š„ + 12 + 20š„ ā 12)/(35š„ + 20 ā 35š„ + 21) = 41š„/41 = x Thus, fog = x = IA Since fog = IA and gof = IB, Hence proved
