Table of contents
- 0. Functions7h 52m
- Introduction to Functions16m
- Piecewise Functions10m
- Properties of Functions9m
- Common Functions1h 8m
- Transformations5m
- Combining Functions27m
- Exponent rules32m
- Exponential Functions28m
- Logarithmic Functions24m
- Properties of Logarithms34m
- Exponential & Logarithmic Equations35m
- Introduction to Trigonometric Functions38m
- Graphs of Trigonometric Functions44m
- Trigonometric Identities47m
- Inverse Trigonometric Functions48m
- 1. Limits and Continuity2h 2m
- 2. Intro to Derivatives1h 33m
- 3. Techniques of Differentiation3h 18m
- 4. Applications of Derivatives2h 38m
- 5. Graphical Applications of Derivatives6h 2m
- 6. Derivatives of Inverse, Exponential, & Logarithmic Functions2h 37m
- 7. Antiderivatives & Indefinite Integrals1h 26m
0. Functions
Combining Functions
4:34 minutes
Problem 88e
Textbook Question
Textbook QuestionComposition of even and odd functions from tables Assume ƒ is an even function, g is an odd function, and both are defined at 0. Use the (incomplete) table to evaluate the given compositions. <IMAGE>
e. g(g(-1))
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Key Concepts
Here are the essential concepts you must grasp in order to answer the question correctly.
Even and Odd Functions
Even functions are defined by the property f(x) = f(-x) for all x in their domain, meaning their graphs are symmetric about the y-axis. Odd functions satisfy the condition g(x) = -g(-x), indicating that their graphs are symmetric about the origin. Understanding these properties is crucial for evaluating compositions of such functions.
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Properties of Functions
Function Composition
Function composition involves applying one function to the result of another, denoted as (f ∘ g)(x) = f(g(x)). In this context, evaluating g(g(-1)) means first finding g(-1) and then using that result as the input for g again. Mastery of this concept is essential for solving the problem at hand.
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Evaluate Composite Functions - Special Cases
Evaluating Functions at Specific Points
To evaluate a function at a specific point, you substitute the point into the function's expression. For example, to find g(-1), you would look up the value of g at -1 from the provided table. This step is fundamental in determining the output of the function compositions required in the question.
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Evaluating Composed Functions
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