3) Let f'be the function given by (x-1)(x²-4). For what positive values of a is f continuous for all real numbers x? 2 x-a (A) none (B) 1 only (C) 2 only (D) 4 only (E) 1 and 4 only
3) Let f'be the function given by (x-1)(x²-4). For what positive values of a is f continuous for all real numbers x? 2 x-a (A) none (B) 1 only (C) 2 only (D) 4 only (E) 1 and 4 only
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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![3) Let f'be the function given by (x-1)(x²-4). For what positive values of a is f continuous for all real numbers x?
2
x²-a
(A) none
(B) 1 only
(C) 2 only
(D) 4 only
(E) 1 and 4 only](/v2/_next/image?url=https%3A%2F%2Fcontent.bartleby.com%2Fqna-images%2Fquestion%2F6bb29282-63cc-412a-a2dd-5fc661270035%2F9cf4aa50-2f69-49dd-a713-5ca1faef88fc%2Fslmp4f_processed.png&w=3840&q=75)
Transcribed Image Text:3) Let f'be the function given by (x-1)(x²-4). For what positive values of a is f continuous for all real numbers x?
2
x²-a
(A) none
(B) 1 only
(C) 2 only
(D) 4 only
(E) 1 and 4 only
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But if a = 4, then we will have a removable discontinuity since the x^2 - 4 in the numerator will cancel with the x^2 - 4 in the denominator leaving f(x) = x - 1 with holes at (2, 1) and (-2, -3). There is no information given that the function is defined at those points, so it remains discontinuous, right?
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