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
Function Operations
2:05 minutes
Problem 19b
Textbook Question
Textbook QuestionFor the pair of functions defined, find (ƒ+g)(x).Give the domain of each. See Example 2. ƒ(x)=3x+4, g(x)=2x-5
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Key Concepts
Here are the essential concepts you must grasp in order to answer the question correctly.
Function Addition
Function addition involves combining two functions by adding their outputs for each input value. For functions ƒ(x) and g(x), the sum (ƒ+g)(x) is defined as (ƒ+g)(x) = ƒ(x) + g(x). This operation is fundamental in algebra as it allows for the creation of new functions from existing ones.
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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. For polynomial functions like ƒ(x) = 3x + 4 and g(x) = 2x - 5, the domain is typically all real numbers, as there are no restrictions such as division by zero or square roots of negative numbers.
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Linear Functions
Linear functions are functions of the form ƒ(x) = mx + b, where m is the slope and b is the y-intercept. They graph as straight lines and have constant rates of change. In this case, both ƒ(x) and g(x) are linear functions, which simplifies the process of finding their sum and understanding their behavior.
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