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Mathematics - Lecture 14: Functions: Domain, range, operations

Mathematics - Lecture 14 "Functions: Domain, range, operations" presents the following content: Relations, functions, finding the (natural) domain of a function, operations on functions, composition of functions, applications of functions. | Functions: Domain, Range, Operations Mathematics 17 Institute of Mathematics, University of the Philippines-Diliman Lecture 14 Math 17 (UP-IMath) Functions Lec. 14 1 / 26 Relations Recall: X × Y = {(x, y) | x ∈ X and y ∈ Y } Math 17 (UP-IMath) Functions Lec. 14 2 / 26 Relations Recall: X × Y = {(x, y) | x ∈ X and y ∈ Y } Definition A relation is a non-empty set of ordered pairs. A relation from X to Y is a non-empty subset of X × Y . Math 17 (UP-IMath) Functions Lec. 14 2 / 26 Relations Recall: X × Y = {(x, y) | x ∈ X and y ∈ Y } Definition A relation is a non-empty set of ordered pairs. A relation from X to Y is a non-empty subset of X × Y . Example. Let X = {x1 , x2 , x3 , x4 }, Y = {y1 , y2 , y3 , y4 }, R = {(x2 , y1 ), (x2 , y2 ), (x3 , y3 )}. Math 17 (UP-IMath) Functions Lec. 14 2 / 26 Relations Recall: X × Y = {(x, y) | x ∈ X and y ∈ Y } Definition A relation is a non-empty set of ordered pairs. A relation from X to Y is a non-empty subset of X × Y . Example. Let X = {x1 , x2 , x3 , x4 }, Y = {y1 , y2 , y3 , y4 }, R = {(x2 , y1 ), (x2 , y2 ), (x3 , y3 )}. Since R ⊆ X × Y , and R = ∅, Math 17 (UP-IMath) Functions Lec. 14 2 / .