hmk3 - (n(x =(3x 5(5x 8 4 Let f A → B and g B → C...

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COT 3100 Fall ’00 Homework #3 Assigned: 10/3/00 Due: 10/12/00 1) Find the inverse of each of the following functions: (The domain is the set of real number unless otherwise specified.) a) f(x) = 12x –7 b) f(x) = (3x+1)/(x-2), for x 2 c) f(x) = 2 x+4 What are the domains and ranges for each of these inverse functions? 2) Compute each of the following function compositions: a) f(x) = 3x+7, g(x)=x 2 , compute g(f(x)). b) f(x) = 2 3x – 2 , g(x)=(x+2)/3, compute f(g(x)). c) f(x) = (4x 2 – 5)/(3x+2), g(x) = x – 4, compute f(g(x)). 3) Define f (n) (x) as f(f(. ..f(x). ..)), where you compose the function f with itself n times. Let f(x) = 1/(x+1). What is the smallest value of n such that f
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Unformatted text preview: (n) (x) = (3x+5)/(5x+8). 4) Let f : A → B and g: B → C denote two functions. If both f and g are surjective, prove that the composition g ° f: A → C is a surjection as well. 5 ) Prove or disprove: If a relation R, defined as a subset of A x A, is symmetric, then show that R ° R is symmetric as well. 6) Given the set A = {2, 4, 6, 8, 10}, define a relation R over A such that R = {(a,b)| a ∈ A ∧ b ∈ A ∧ |b – a| = 4} a) Use a directed graph to depict the relation R above. b) Determine if the relation R is (i)reflexive, (ii)irreflexive, (iii)symmetric, (iv)anti-symmetric, and (v)transitive....
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