75. Show that if a function f is defined on an interval symmetric aboutthe origin (so that f is defined at -x whenever it is defined at x), thenf(x) + f(-x) , f(x) – f(-x)f(x) =(1)22Then show that (f(x) + f(-x))/2 is even and that (f(x) –f(-x))/2 is odd.

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Answered: 75. Show that if a function f is…

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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Apply Corollary 2 to the Intermediate Value Theorem. f is a polynomial and continuous everywhere. f(-3) = 170, f(-2) = -25, f(-1) = 2, f(0) = -1, f(l) = 2, f(2) = -25, and f(3) = 170. Thus, f has a zero in each of these intervals: (-3, -2), (-2, -1), (-1, 0), (0, 1) , (1, 2), (2, 3), and f must have six distinct solutions.
The function f(x) has a domain of [-9, 9] and is plotted below such that the portion of the graph on the interval (-2, 1) is hidden from view. Given that f(-2) = −3 and f(1) = 5, determine what conclusions can be drawn based on the Intermediate Value Theorem on the interval (-2, 1). -10-9-8-7 -6 -5 -4 -3 -2 Since the function f(x) is | Intermediate Value Theorem y ? ? ? ? ? ? r I r 1 I L I L I I 2 19 3 Graph of f 4 5 6 7 8 9 10 X ✓on its domain, the
Suppose that f(x) is function with f(5) = -8 and f(9) = 8. Determine which choice best describes the following statement “f(x) = 0 for some x in the interval [5, 9]”
Suppose that the functions fand g are defined as follows. f(x) = -5x² +1 g (x) = Vx+3 Find f-g and f· g. Then, give their domains using interval notation. (f- 2)(+) = 0 G (0,0) (0,0) Domain of f - g :0 OvO (0,0) (0,0) 00 -00 (*3)(;) = 0 ? Domain of f g
all the options are: is or is not
let f(x)={x^2+2, x >-1 AND -x^2-x, x less than for equal to -1} compute f(0), f(-1)and f(-2) a. 0, 2, 6 b. 2, 0, 6 c. 2, 2, 6 d. 2, 0, -2 e. 0, 1, -2
Consider the following function. F(x) = x^4 + x^3- 20x^2 Find all values of x such that f(x) > 0. (-00, -5) U (4, 00) [-5, 0) U (0, 4) (-5, 4) (-5, 0) U (0, 4) (-00, -5) U [4,00) Find all values of x such that f(x) < 0. (-00, -5) U [4, 00) (-00, -5) U (4, 00) (-5, 4) [-5, 0) U (0, 4) (-5, 0) U (0, 4) How do you solve this?

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75. Show that if a function f is defined on an interval symmetric about the origin (so that f is defined at -x whenever it is defined at x), then f(x) + f(-x) , f(x) – f(-x) f(x) = (1) 2 2 Then show that (f(x) + f(-x))/2 is even and that (f(x) – f(-x))/2 is odd.