The functions f and g are both defined on the domain of all real numbers with f(x) = x^3 and g(x) = 5x + 2. (a) Write equations for the functions f ◦ g and g ◦ f. (b) h(x) = (1/5x+2)^3 . What are the domain and range of h? (c) Find an equation for a function, k, so that h is equal to ONE of these compositions: f ◦ k, k ◦ f, g ◦ k, k ◦ g, or f ◦ k ◦ g. Be sure to show how your composition results in h.
The functions f and g are both defined on the domain of all real numbers with f(x) = x^3 and g(x) = 5x + 2. (a) Write equations for the functions f ◦ g and g ◦ f. (b) h(x) = (1/5x+2)^3 . What are the domain and range of h? (c) Find an equation for a function, k, so that h is equal to ONE of these compositions: f ◦ k, k ◦ f, g ◦ k, k ◦ g, or f ◦ k ◦ g. Be sure to show how your composition results in h.
Calculus: Early Transcendentals
8th Edition
ISBN:9781285741550
Author:James Stewart
Publisher:James Stewart
Chapter1: Functions And Models
Section: Chapter Questions
Problem 1RCC: (a) What is a function? What are its domain and range? (b) What is the graph of a function? (c) How...
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The functions f and g are both defined on the domain of all real numbers with f(x) = x^3 and g(x) = 5x + 2.
(a) Write equations for the functions f ◦ g and g ◦ f.
(b) h(x) = (1/5x+2)^3 . What are the domain and range of h?
(c) Find an equation for a function, k, so that h is equal to ONE of these compositions: f ◦ k, k ◦ f, g ◦ k, k ◦ g, or f ◦ k ◦ g. Be sure to show how your composition results in h.
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