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

1:40 minutes

Problem 59a

Textbook Question

Let ƒ(x)=2x-3 and g(x)=-x+3. Find each function value. See Example 5. (ƒ∘g)(-2)

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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. The notation (ƒ∘g)(x) means to apply g first and then apply f to the result. This process requires substituting the output of g into the function f, which is essential for solving problems that involve multiple functions.

Evaluating Functions

Evaluating a function means finding the output value for a given input. For example, to evaluate g(-2), you substitute -2 into the function g(x) and calculate the result. This step is crucial in function composition, as the output of the first function becomes the input for the second function.

Linear Functions

Linear functions are mathematical expressions of the form f(x) = mx + b, where m is the slope and b is the y-intercept. Both ƒ(x) and g(x) in this problem are linear functions, which means their graphs are straight lines. Understanding their properties helps in evaluating and composing these functions effectively.