Download Operations of Functions Worksheet

Pre-Calculus/Trig 3
Function Combinations Worksheet
Name ________________________
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) =
2
and g(x) = x2 – 2. Find each of the following functions.
x4
7. (f + g)(x)
8. (f – g)(x)
10. (f/g)(x)
11. Find (f◦g)(x) and (g◦f)(x)
f(x) = 1/3 x + 5
g(x) = x – 3
9. (fg)(x)
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
p (t )
interpret h(t ) 
.
n(t )
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
A(t )  3.36t 2  59.8t  735 and N (t )  1.95t 2  42.2t  603 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.