f(x) x³+x²-18x +4. Over which of these domains could you define f-¹(x)? Remember that f(x) must be one-to-one (only one y-value for each x-value) over the domain where f-1(x) is defined as a function. So, in some cases you must restrict the domain of f(x) so that it's one-to-one. There might be more than one section of domain that's one-to-one. HINT: The function f(x) is one-to-one wherever it's monotonic ("monotonic" simply means increasing or decreasing over the entire interval, so the derivative does not change sign). To find these intervals, start by taking the first derivative, which is '(x) = 3x² + 3x - 18, and setting it equal to zero. 1. (-∞, -3] II. [-3, 0⁰) III. [2, ∞) 1 || ||| Either I or II Either I or III
f(x) x³+x²-18x +4. Over which of these domains could you define f-¹(x)? Remember that f(x) must be one-to-one (only one y-value for each x-value) over the domain where f-1(x) is defined as a function. So, in some cases you must restrict the domain of f(x) so that it's one-to-one. There might be more than one section of domain that's one-to-one. HINT: The function f(x) is one-to-one wherever it's monotonic ("monotonic" simply means increasing or decreasing over the entire interval, so the derivative does not change sign). To find these intervals, start by taking the first derivative, which is '(x) = 3x² + 3x - 18, and setting it equal to zero. 1. (-∞, -3] II. [-3, 0⁰) III. [2, ∞) 1 || ||| Either I or II Either I or III
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...
Related questions
Question
Expert Solution
This question has been solved!
Explore an expertly crafted, step-by-step solution for a thorough understanding of key concepts.
This is a popular solution!
Trending now
This is a popular solution!
Step by step
Solved in 4 steps
Recommended textbooks for you
Calculus: Early Transcendentals
Calculus
ISBN:
9781285741550
Author:
James Stewart
Publisher:
Cengage Learning
Thomas' Calculus (14th Edition)
Calculus
ISBN:
9780134438986
Author:
Joel R. Hass, Christopher E. Heil, Maurice D. Weir
Publisher:
PEARSON
Calculus: Early Transcendentals (3rd Edition)
Calculus
ISBN:
9780134763644
Author:
William L. Briggs, Lyle Cochran, Bernard Gillett, Eric Schulz
Publisher:
PEARSON
Calculus: Early Transcendentals
Calculus
ISBN:
9781285741550
Author:
James Stewart
Publisher:
Cengage Learning
Thomas' Calculus (14th Edition)
Calculus
ISBN:
9780134438986
Author:
Joel R. Hass, Christopher E. Heil, Maurice D. Weir
Publisher:
PEARSON
Calculus: Early Transcendentals (3rd Edition)
Calculus
ISBN:
9780134763644
Author:
William L. Briggs, Lyle Cochran, Bernard Gillett, Eric Schulz
Publisher:
PEARSON
Calculus: Early Transcendentals
Calculus
ISBN:
9781319050740
Author:
Jon Rogawski, Colin Adams, Robert Franzosa
Publisher:
W. H. Freeman
Calculus: Early Transcendental Functions
Calculus
ISBN:
9781337552516
Author:
Ron Larson, Bruce H. Edwards
Publisher:
Cengage Learning