Ex 1.3, 10 - Chapter 1 Class 12 Relation and Functions
Last updated at Dec. 16, 2024 by Teachoo
Last updated at Dec. 16, 2024 by Teachoo
Ex 1.3, 10 Let f: X → Y be an invertible function. Show that f has unique inverse. (Hint: suppose g1 and g2 are two inverses of f. Then for all y ∈ Y, fog1(y) = IY(y) = fog2(y). Use one-one ness of f). Let f: X → Y be an invertible function. If g is an inverse of f, then for all y ∈ Y fog(y) = IY Let g1 & g2 be two inverses of f Then, for all y ∈ Y, fog1(y) = IY & fog2(y) = IY ⇒ fog1(y) = fog2(y) f (g1(y)) = f (g2(y)) Since f is invertible, f is one-one. So, if f(x1) = f(x2), then x1 = x2 Since f (g1(y)) = f (g2(y)), ∴ g1(y) = g2(y) ⇒ g1 = g2 Hence, f has a unique inverse.
Inverse of a function
Ex 1.3, 2
Ex 1.3, 3 (i) Important
Ex 1.3, 3 (ii)
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Ex 1.3, 5 (i)
Ex 1.3, 5 (ii) Important
Ex 1.3, 5 (iii) Important
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Ex 1.3 , 8 Important
Ex 1.3 , 9 Important
Ex 1.3, 10 Important You are here
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Ex 1.3, 13 (MCQ) Important
Ex 1.3, 14 (MCQ) Important
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