Perform the indicated operation.

Slides:

Advertisements

Similar presentations

2.3 Combinations of Functions Introductory MATHEMATICAL ANALYSIS For Business, Economics, and the Life and Social Sciences (12 th Edition) Copyright ©

Advertisements

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.

Composition of Functions

1.7, page 209 Combinations of Functions; Composite Functions Objectives Find the domain of a function. Combine functions using algebra. Form composite.

Jeopardy 100 Composite Functions Combining Functions Combining Functions Inverse Functions and Relations.

Function Operations Add or subtract functions. 2.Multiply functions. Composite Functions Find the composition of two 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.

7-3 NOTES Algebra II. Starter Given that f(x) = 3x – 2, and g(x) = 2x 2, f(x) – g(x) = f(x) *g(x) g(f(x)) =

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))

DO NOW: 6.3: w/s C: Perform the indicated operation. 1.) Find g(f(x)) if f(x) = 2x 2 – x and g(x) = 2.) Find g(h(8)) if g(x) = -x 2 and h(x) =

Final Exam Schedule – Fall, :00 ClassThursday, December 1110:30 – 12:30 2:00 ClassThursday, December 111:00 – 3:00 3:30 ClassTuesday, December 93:30.

Chapter 7 7.6: Function Operations. Function Operations.

Translations and Combinations Algebra 5/Trigonometry.

5.1 Composite Functions Goals 1.Form f(g(x)) = (f  g) (x) 2.Show that 2 Composites are Equal.

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.

Math on the Mind. Composition of Functions Unit 3 Lesson 7.

Suppose also that you were not told the details of those separate charges, but only that the function C(n) = 1.25(55n + 300) gives total cost of the event.

6-1: Operations on Functions (Composition of Functions)

Composite Functions How would you define composite functions? Math30-1.

Lesson 2-8: Operations of Functions

Do Now: Find f(g(x)) and g(f(x)). f(x) = x + 4, g(x) = x f(x) = x + 4, g(x) = x

Warm-Up . Homework Questions Domain Algebraically Pre-Calculus Mrs. Ramsey.

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)

Do Now: Perform the indicated operation.

Operations with Functions

LESSON 1-2 COMPOSITION OF FUNCTIONS

3.5 Operations on Functions

Digital Lesson Algebra of Functions.

DO NOW: Perform the indicated operation.

Composition of Functions

Copyright 2013, 2009, 2005, 2001, Pearson Education, Inc.

Today in Pre-Calculus Notes: (no handout) Go over quiz Homework

Composition of Functions 1.

Functions Review.

Section 5.1 Composite Functions.

Homework Questions.

= + 1 x x2 - 4 x x x2 x g(x) = f(x) = x2 - 4 g(f(x))

Combinations of Functions:

Activity 2.8 Study Time.

Homework Questions.

Function Composition Section 8-7.

Composition of Functions And Inverse Functions.

2.6 Operations on Functions

Combinations of Functions

Operations with Functions

3.5 Operations on Functions

Function Operations Function Composition

Warm Up Determine the domain of the function.

Function Composition Section 8-7.

Determine if 2 Functions are Inverses by Compositions

Function Composition.

Homework Questions.

Use Inverse Functions Notes 7.5 (Day 2).

6.3 Perform Function Operations & Composition

Function Operations Function Composition

Replace inside with “x” of other function

Section 6.1 Composite Functions.

L7-6 Obj: Students will add, subtract, multiply and divide functions

Operations on Functions

Do Now: Given: Express z in terms of x HW: p.159 # 4,6,8,

Evaluate x = 3; 2x + 6.

Aim: How do we do arithmetic with functions?

12 Chapter Chapter 2 Exponential and Logarithmic Functions.

Algebra 2 Ch.7 Notes Page 52 P Function Operations.

Composition of Functions

Presentation transcript:

Perform the indicated operation. Let f(x) = x+5 and g(x) = x2 – 5x + 2 Find f(x) + g(x) Let f(x) = -3x1/3 + 4x1/2 & g(x) = 5x1/3 + 4x1/2 Find f(x) – g(x)

6.3: Perform Function Operations and Compositions Algebra II 6.3: Perform Function Operations and Compositions HW: p.432 (20-26 even), p.445 (1-4)

Perform the indicated operation. Let f(x) = 4x2/3 and g(x) = 5x1/2 1.) Find g(x) . f(x) 2.) Find g(x)/f(x)

Find the indicated value. (composition of functions) Let f(x) = 4x + 7 and g(x) = 12x – 1 1.) Find g(f(3)) 2.) Find f(g(3))

Find the indicated value. Let g(x) = -x2 and h(x) = 1.) Find h(h(-4)) 2.) Find g(h(8))

Perform the indicated operation. Let f(x) = 4x and g(x) = 3x – 5 Find f(g(x))

Perform the indicated operation. Let f(x) = 2x2 and g(x) = 3x – 5 Find f(g(x))

Perform the indicated operation. Let f(x) = 3x-1 , g(x) = 2x – 7 , and h(x) = 1.) Find g(f(x)) 2.) Find g(h(x))

Perform the indicated operation. Let f(x) = 2x2 + 5 and g(x) = x – 8 Find f(g(x))

Perform the indicated operation. Let f(x) = 2x – 4 and g(x) = 5x + 8 Find g(f(x))