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
Chapter5: Polynomial And Rational Functions
Section5.3: Graphs Of Polynomial Functions
Problem 2TI: Use the graph of the function of degree 5 in Figure 10 to identify the zeros of the function and...
Related questions
Question
![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 f'(x) = 3x² + 3x - 18,
and setting it equal to zero.
1. (-∞, -3]
II. [-3, ∞)
III. [2, ∞)
||
|||
Either I or II
Either I or III](/v2/_next/image?url=https%3A%2F%2Fcontent.bartleby.com%2Fqna-images%2Fquestion%2F6bed085c-3ecb-47a6-9147-a081ba32700e%2Fb4d9402c-0b3e-4d7c-b0f2-f337595d450c%2Ffqn40d_processed.png&w=3840&q=75)
Transcribed Image Text: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 f'(x) = 3x² + 3x - 18,
and setting it equal to zero.
1. (-∞, -3]
II. [-3, ∞)
III. [2, ∞)
||
|||
Either I or II
Either I or III
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