Applications and Investigations in Earth Science (9th Edition)
Applications and Investigations in Earth Science (9th Edition)
9th Edition
ISBN: 9780134746241
Author: Edward J. Tarbuck, Frederick K. Lutgens, Dennis G. Tasa
Publisher: PEARSON
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14. Define the concept of an equivalent relation. A relation R is defined on the set Z, of integers, by:a R b a- a= b² – b. show that R is an equivalence relation. Write down 3 elements of the relation R, where a R b but a + b. 15. A real valued function f is defined by f: x → 2х-3 X E R, x # -1 X+1 a) Obtain the composite function ff and state its domain b) Show that f is injective c) Find the range of f and deduce that f is not surjective 16. The functions f and g are defined by x+1 f: x→*-, x € R, x # 3 | 2x+3 2 g: x→3x +2,x E R. a) Express, in a similar manner, the function (gf)-1 b) Obtain an element in the domain of g which is invariant under g. 17. i) The functions f and g are defined on R, the set of real numbers, by f: x H – , x # 1 and g: x 2x – 3. X-1 Find the composite function f og, stating its domain. ii) A binary relation R is defined on the set of integers, by: xRy x - y = 3c, wherec is an integer. Prove that R is an equivalence relation. 18. A function f: R → R is defined by f: x → 3x 1 Determine whether or not f is 2x+1 2 surjective. 19. The function f: R R is defined by (x) = 1 x3 . Find the monotony of f, showing | 3 clearly its variation table
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Transcribed Image Text:14. Define the concept of an equivalent relation. A relation R is defined on the set Z, of integers, by:a R b a- a= b² – b. show that R is an equivalence relation. Write down 3 elements of the relation R, where a R b but a + b. 15. A real valued function f is defined by f: x → 2х-3 X E R, x # -1 X+1 a) Obtain the composite function ff and state its domain b) Show that f is injective c) Find the range of f and deduce that f is not surjective 16. The functions f and g are defined by x+1 f: x→*-, x € R, x # 3 | 2x+3 2 g: x→3x +2,x E R. a) Express, in a similar manner, the function (gf)-1 b) Obtain an element in the domain of g which is invariant under g. 17. i) The functions f and g are defined on R, the set of real numbers, by f: x H – , x # 1 and g: x 2x – 3. X-1 Find the composite function f og, stating its domain. ii) A binary relation R is defined on the set of integers, by: xRy x - y = 3c, wherec is an integer. Prove that R is an equivalence relation. 18. A function f: R → R is defined by f: x → 3x 1 Determine whether or not f is 2x+1 2 surjective. 19. The function f: R R is defined by (x) = 1 x3 . Find the monotony of f, showing | 3 clearly its variation table
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