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
4:56 minutes
Problem 23
Textbook Question
Textbook QuestionFor the pair of functions defined, find (ƒ+g)(x). Give the domain of each. See Example 2. ƒ(x)=√(4x-1), g(x)=1/x
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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 the functions ƒ(x) and g(x), the sum (ƒ+g)(x) is defined as ƒ(x) + g(x). This operation requires that both functions are defined for the same input values, which is crucial for determining the overall domain of the resulting function.
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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 ƒ(x)=√(4x-1), the expression under the square root must be non-negative, leading to the condition 4x-1 ≥ 0. For g(x)=1/x, the function is undefined when x=0. The overall domain of (ƒ+g)(x) is the intersection of the domains of ƒ(x) and g(x).
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Square Root Function
The square root function, denoted as √(x), returns the non-negative value whose square equals x. It is only defined for non-negative inputs, meaning that any expression under the square root must be greater than or equal to zero. In this case, the function ƒ(x)=√(4x-1) requires that 4x-1 ≥ 0, which directly influences the domain of the function.
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