University:
Montgomery College
Course:
MATH 165: Precalculus
Academic year:

2020
Views:

418

Pages:

8
Author:

Raina Flores

Math 165 – Section 5.1 – Composition of functions 1) Write the definition – section 5.1, page 258, new edition. (f o g) (x) = 2) Composition: “x goes into g”, “the output from g is the input into f”. Look at the tables A, B, and C above. a) Show how you go from the number 1 listed on table A, to the number 4 in table B. b) Show how you go from the number 4 in table B to the number -1 in table C. c) If we put together steps (a) and (b) above, we can say that (f o g) (1) = f(g(1)) = f(4) = -1. This means, first we evaluate g(1) = 3(1) + 1 = 4; then evaluate f(4) = (1/2)(4) – 3 = -1. Now, using the same diagram above, complete the following: a. What is (f o g)(3)? b. What is (f o g)(7)? 3) Given f(x) = 2x – 7 and g(x) = -3x + 1, show all work to find each of the following: a. Find (f o g) (-2) b. Find (g o f)(-1) 1 What is composition? Putting one function into another – where? In the “variable place” of the other 2 4) In the real world there are many situations in which some quantity depends on a variable which at the same time, depends on another variable. a) What will be the area of the spill after 2 minutes? After 5 minutes? After t-minutes? b) NOTE: (we’ll do in class) 4 3 5) The volume of a balloon is given by 𝑉𝑉(𝑟𝑟) = 𝜋𝜋𝑟𝑟 3 and the radius is increasing with time, in seconds, according to 1 the formula: 𝑟𝑟(𝑡𝑡) = 2 𝑡𝑡 3 . a) What is the volume of the balloon after 3 seconds? After 5 seconds? After t seconds? c) NOTE: (we’ll do in class) 3 6) Use the values in the table to evaluate the indicated composition of functions. 7) Use the graphs to evaluate the composition of functions. 4 8) Find the composite function and its domain. Also, make up some evaluation problems using the given functions. 5 9) Find the components f and g, so that H = fog 10) Applications 6 7 Functions from Functions (Professor McCullough) 2 Let f ( x ) = x ; g ( x ) = 1 x ; h ( x ) = x ; k ( x ) = e ; A ( x ) = ln ( x ) x Express each of the following as a combination of the functions above. Use the operations addition, subtraction, multiplication, division and composition. 1. e 3. x ex x2 5. e ln ( x ) 4. x 2 + x x 6. ln ( x ) − e ( 1  x 8. ln x 2 + x2 + ex 10. 7. ln  9. 2. x 2 e x ex 2 x ) − x 8