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
2:47 minutes
Problem 17Lial - 13th Edition
Textbook Question
Textbook QuestionLet ƒ(x)=x^2+3 and g(x)=-2x+6. Find each of the following. See Example 1. (ƒ/g)(-1)
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Key Concepts
Here are the essential concepts you must grasp in order to answer the question correctly.
Function Notation
Function notation is a way to represent mathematical functions in a clear format. For example, f(x) denotes a function f evaluated at the input x. Understanding how to read and interpret function notation is essential for performing operations on functions, such as addition, subtraction, multiplication, and division.
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Division of Functions
The division of functions involves creating a new function that represents the ratio of two existing functions. If f(x) and g(x) are two functions, then (f/g)(x) = f(x)/g(x). This concept is crucial for evaluating the combined function at specific values, ensuring that the denominator is not zero to avoid undefined expressions.
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Multiplying & Dividing Functions
Evaluating Functions
Evaluating functions means substituting a specific value into the function to find the output. For instance, to find (f/g)(-1), you first calculate f(-1) and g(-1), then divide the results. This process is fundamental in algebra, as it allows for the analysis of function behavior at particular points.
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Related Practice
Textbook Question
Without using paper and pencil, evaluate each expression given the following functions. ƒ(x)=x+1 and g(x)=x^2
(ƒ+g)(2)
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Function Operations practice set
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