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
10:10 minutes
Problem 44
Textbook Question
Textbook QuestionIn Exercises 31–50, find ƒ+g, f−g, fg, and f/g. Determine the domain for each function. f(x)= = (3x+1)/(x² - 25), g(x) = (2x -4)/(x² - 25)
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Key Concepts
Here are the essential concepts you must grasp in order to answer the question correctly.
Function Operations
Function operations involve combining two functions through addition, subtraction, multiplication, and division. For example, if f(x) and g(x) are two functions, then f+g means adding their outputs, while f-g means subtracting the output of g from f. Understanding these operations is crucial for manipulating and analyzing functions in algebra.
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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 rational functions, like those given in the question, the domain is restricted by values that make the denominator zero. Identifying the domain is essential to ensure that the operations performed on the functions yield valid results.
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Rational Functions
Rational functions are ratios of two polynomials, expressed in the form f(x) = P(x)/Q(x), where P and Q are polynomials. The behavior of rational functions, including their domains and asymptotes, is influenced by the degrees and coefficients of the polynomials. Understanding rational functions is key to solving problems involving function operations and determining their domains.
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