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
College Algebra (MindTap Course List)
12th Edition
ISBN:9781305652231
Author:R. David Gustafson, Jeff Hughes
Publisher:R. David Gustafson, Jeff Hughes
Chapter4: Polynomial And Rational Functions
Section4.1: Quadratic Functions
Problem 6SC: A company that makes and sells baseball caps has found that the total monthly cost C in dollars of...
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