Table of contents
- 0. Review of Algebra4h 16m
- 1. Equations & Inequalities3h 18m
- 2. Graphs of Equations43m
- 3. Functions2h 17m
- 4. Polynomial Functions1h 44m
- 5. Rational Functions1h 23m
- 6. Exponential & Logarithmic Functions2h 28m
- 7. Systems of Equations & Matrices4h 6m
- 8. Conic Sections2h 23m
- 9. Sequences, Series, & Induction1h 19m
- 10. Combinatorics & Probability1h 45m
3. Functions
Intro to Functions & Their Graphs
1:28 minutes
Problem 73
Textbook Question
Textbook QuestionGiven functions f and g, find (a)(ƒ∘g)(x) and its domain. See Examples 6 and 7. ƒ(x)=-6x+9, g(x)=5x+7
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Key Concepts
Here are the essential concepts you must grasp in order to answer the question correctly.
Function Composition
Function composition involves combining two functions, where the output of one function becomes the input of another. In this case, (ƒ∘g)(x) means applying g first and then applying f to the result of g. This process is essential for evaluating the composite function and understanding how the two functions interact.
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Domain of a Function
The domain of a function is the set of all possible input values (x-values) for which the function is defined. When finding the domain of a composite function, it is crucial to consider the domains of both individual functions and any restrictions that may arise from the composition process, such as division by zero or square roots of negative numbers.
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Linear Functions
Linear functions are polynomial functions of degree one, represented in the form f(x) = mx + b, where m is the slope and b is the y-intercept. In this question, both f(x) and g(x) are linear functions, which means their graphs are straight lines. Understanding their properties helps in analyzing their composition and determining the resulting function's behavior.
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