**Question 1.** Suppose $ A = \{a, b, c\} $. Let $ f : A \to A $ be defined by $ f(a) = c $, $ f(b) = a $ and $ f(c) = b $. Also, let $ g : A \to A $ be defined by $ g(a) = b $, $ g(b) = c $, and $ g(c) = a $.i) Write the assignment rules for the functions $ f \circ g $ and $ g \circ f $.ii) Determine the inverse function of $ f $.iii) Determine the inverse function of $ g $.

The function f is an inverse of g or g is an inverse of f if fog=I and gof=I.

Answered: Question 1. Suppose A = {a, b, c}. Let…

Advanced Engineering Mathematics

10th Edition

ISBN:9780470458365

Author:Erwin Kreyszig

Publisher:Erwin Kreyszig

Chapter2: Second-order Linear Odes

Section: Chapter Questions

Problem 1RQ

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Consider the functions f : A → B, g : B → A and h : B → A such that if gf =14 and fh = 1B. Prove f is a 1-1 correspondence A - B. fla = f and 18f = f. (a) (b)
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Which of the following relation is a function? a) Z={(1,4), (2,3), (3,2). (2,4), (1,4), (1,5 )} b) s={(- 2,1) (- 1,2) (1,2) (2,1) (3,4). (5,7)} c) A={1,3). (2. – 5 ). (1.5). (- 3,1) (- 2,–2).} d) M = {(2.1) (5.1) (8,1) (11.1). (1.1) (2.5)}

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