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Chapter 7 7.6: Function Operations
Example O If f(x) = 3x + 8 & g(x) = 2x – 12, O find (f + g) & (f – g) and their domains
Example O If f(x) = 5x² - 4x & g(x) = 5x + 1 O Find (f + g) & (f – g) and their domains
Example O If f(x) = x² - 1 and g(x) = 5x + 1, O Find f ∙ g & f/g and their domains
Example O If f(x) = 6x² + 7x – 5 & g(x) = 2x – 1, O Find f ∙ g & f/g and their domains
Composite Functions O Composite Functions: When you apply one function (g(x)) after another function (f(x)) O (g ◦ f)(x) = g(f(x))
Example O Let f(x) = x – 2 and g(x) = x² O Find (g ◦ f)(-5) O Method 1: O Method 2:
Example O Let f(x) = x – 2 and g(x) = x² O Find (f ◦ g)(-5) O Method 1: O Method 2:
Example O Let f(x) = 3x + 1 and g(x) = 2x² + 1 O Find f(g(-1)) O Method 1: O Method 2:
Assignment O p. 394-395 O 13-19, 22-38 evens
2.3 Combinations of Functions Introductory MATHEMATICAL ANALYSIS For Business, Economics, and the Life and Social Sciences (12 th Edition) Copyright ©
Domain: 1) f(0) = 8 2) f(3) = 3) g(-2) = -2 4) g(2) = 0 5) f(g(0)) = f(2) =0 6) f(g(-2)) = f(-2) =undefined 7) f(g(2)) = f(0) =8 8) f(g(-1)) = f(1) =3.
Function Composition Fancy way of denoting and performing SUBSTITUTION But first …. Let’s review.
Composite Functions. Objectives Add, subtract, multiply, and divide functions. Find compositions of one function with another function.
Chapter 3: Functions and Graphs 3.5: Operations on Functions
Section 12.1 Composite and Inverse Functions
Warm-up Arithmetic Combinations (f+g)(x) = f(x) + g(x) (f-g)(x) = f(x) – g(x) (fg)(x) = f(x) ∙ g(x) (f/g)(x) = f(x) ; g(x) ≠0 g(x) The domain for these.
Composition of Functions. Definition of Composition of Functions The composition of the functions f and g are given by (f o g)(x) = f(g(x))
Wednesday, March 25 Today's Objectives
Operations on Functions Lesson 3.5. Sums and Differences of Functions If f(x) = 3x + 7 and g(x) = x 2 – 5 then, h(x) = f(x) + g(x) = 3x (x 2 – 5)
Composite Functions. O Finding a composite function simply means plugging one function into another function. O The key thing to remember is which way.
6-1: Operations on Functions (Composition of Functions)
Chapter 3: Transformations of Graphs and Data Lesson 7: Compositions of Functions Mrs. Parziale.
Ch 9 – Properties and Attributes of Functions 9.4 – Operations with Functions.
Aim: What is the composition of functions? Do Now: Given: Express z in terms of x HW: Work sheet.
Function Composition Given f(x) = 2x + 2 and g(x) = 2, find f ºg(x). f ºg(x)=f(g(x)Start on the inside. f(g(x)) g(x) = 2, so replace it. f(g(x)) = f(2)
PreCalculus Section 4.2 Perform operation on functions Like, numbers, functions can be added, subtracted, multiplied, and divided. The profit generated.
Section 2.7 Combining Functions Objectives: To add, subtract, multiply and divide functions. Composition of functions.
Objective: Find inverse functions. Warm up 1. a.Find (f o g)(x). b.Find the domain of f(g(x)).
Ch. 7 Day 6 Book Section 7.6 Function Operations.
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