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 Composition
1:39 minutes
Problem 63b
Textbook Question
Textbook QuestionIn Exercises 51–66, find a. (fog) (x) b. (go f) (x) c. (fog) (2) d. (go f) (2). f(x) = 2x-3, g(x) = (x+3)/2
Verified Solution
This video solution was recommended by our tutors as helpful for the problem above
Video duration:
1mPlay a video:
Was this helpful?
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 to create a new function. If f(x) and g(x) are two functions, the composition (fog)(x) means applying g first and then f to the result, expressed as f(g(x)). Understanding this concept is crucial for solving problems that require evaluating composite functions.
Recommended video:
4:56
Function Composition
Evaluating Functions
Evaluating functions means substituting a specific value into a function to find its output. For example, if f(x) = 2x - 3, evaluating f(2) involves replacing x with 2, resulting in f(2) = 2(2) - 3 = 1. This skill is essential for calculating the values of composite functions at given points.
Recommended video:
4:26
Evaluating Composed Functions
Algebraic Manipulation
Algebraic manipulation refers to the process of rearranging and simplifying expressions using algebraic rules. This includes operations like addition, subtraction, multiplication, and division of functions. Mastery of these techniques is necessary for simplifying composite functions and performing evaluations accurately.
Recommended video:
Guided course
05:09
Introduction to Algebraic Expressions
Watch next
Master Function Composition with a bite sized video explanation from Nick Kaneko
Start learningRelated Videos
Related Practice