Pre-Calculus/Trig 3



Pre-Calculus/Trig 3 Name ________________________

Function Combinations Worksheet

I. Given f(x) = 3x + 2 and g(x) = x2 – 5. Find each of the following functions.

1. (f + g)(x) 2. (f – g)(x) 3. (fg)(x)

4. (f ◦ g)(x) 5. (g ◦ f)(x) 6. (f/g)(x)

II. Given f(x) = [pic] and g(x) = x2 – 2. Find each of the following functions.

7. (f + g)(x) 8. (f – g)(x) 9. (fg)(x)

10. (f/g)(x)

11. Find (f◦g)(x) and (g◦f)(x)

f(x) = 1/3 x + 5

g(x) = x – 3

Applications

12. Let d(t) be the number of dogs in the US in year t, and let c(t) be the number of cats in the US in the year t, where t=0 corresponds to 2000

a. Find the function p(t) that represents the total number of dogs and cats in the US.

b. Interpret the value of p(5).

c. Let n(t) represent the population of the US in year t, where t=0 corresponds to 2000. Find and interpret [pic].

13. The total numbers of Army personnel (in thousands) A and Navy personnel (in thousands) N from 1990 to 2002 can be approximated by the models

[pic] and [pic]where t represents the year, with t=0 corresponding to 1990.

a. Find and interpret (A + N)(t). Evaluate this function for t = 4, 8, and 12

b. Find and interpret (A-N)(t). Evaluate this function for t = 4, 8, and 12.

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