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

College Algebra

3. Functions

Function Composition

1:24 minutes

Problem 51a

Textbook Question

In Exercises 51–66, find a. (fog) (x) b. (go f) (x) c. (fog) (2) d. (go f) (2). f(x) = 2x, g(x) = x+7

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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)). This concept is essential for evaluating expressions like (fog)(x) and (go f)(x).

Evaluating Functions

Evaluating functions means substituting a specific value into a function to find its output. For example, if f(x) = 2x, then f(2) = 2(2) = 4. This process is crucial for finding specific values of composed functions, such as (fog)(2) and (go f)(2).

Algebraic Manipulation

Algebraic manipulation refers to the techniques used to simplify and rearrange algebraic expressions. This includes operations like addition, subtraction, multiplication, and factoring. Mastery of these skills is necessary to effectively compute the results of function compositions and to simplify the expressions obtained from them.