Calculus: Early Transcendentals
8th Edition
ISBN: 9781285741550
Author: James Stewart
Publisher: Cengage Learning
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- Show that if a function has a unique right inverse, then it is necessarily bijective.arrow_forwardLet f : A → B and g : B → C be functions. Prove that if f and g are bijective, theng ◦f is bijective. Let f : A →B and g : B →C be functions.• Prove that if g ◦ f is surjective then g is surjective.• Prove that if g ◦ f is bijective, then f is injective and g is surjective.• Find functions f and g such that g ◦f is bijective but f is not surjective and g is notinjective. Hence the preceding statements are sharp.arrow_forwardLet ƒ : R → R and g : R → R be the functions given by f(x) = 2x³ + 5 g(x) = √√/1/√(x - 5) Verify that f and g are inverses of one another by showing that go f and fo g both equal idr.arrow_forward
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