Second Project

Froemke – Math 95 – Spring 2011 – Project 2 – Project is due May 21

1. If f(x) = 1/(x + 1) and g(x)= x² . Give the following compositions:

a. f(g(x))

b. g(f(x))

c. f(f(x))

d. g(g(g(x)))

2. Use the table to find the following:

t	f(t)	g(t)	p(t)
0	0	-2	-10
1	2	5	-5
2	4	10	0
3	6	13	2
4	8	16	4
10	-20	22	22
12	-10	15	25
15	-3	8	28

1. f(2)
2. f(15) – g(15)
3. (f-g+p)(3)
4. (g*p)(1)
5. (f/p)(2)
6. g(f(2))
7. (f o g)(2)
8. f(p(0))
9. p(f(1))

3) The DaveCo monthly revenue on car-painting robots is 5 million dollars per robot. The cost is (x² + 6) million dollars, where x is the number of robots produced in a month. Remember: Profit is Revenue minus Cost.

a) What’s the DaveCo monthly profit on robots?

b) What’s the best number of robots to produce?

4) The number N of bacteria in a refrigerated food is given by

N(T)=20T² - 80T+500; 2 < T < 14

where T is the temperature of the food (in degrees Celsius). When the food is removed from refrigeration, the temperature is given by

T(t)=4t+2; 0 < t < 3

where t is the time (in hours).

a) Find the composition of N(T(t)) and interpret its meaning in context of the problem.

b) Find the number of bacteria in the food when t=2 hours.

c) Find the time when the bacterial count reaches 2000.

5) One of the two functions below has an inverse:

f(x) = (x-1) / 2

g(x) = x² – 5x + 6

a) Which one does not? Justify your answer.

b) Find the inverse of the one that does.

c) Verify that you’ve found the correct inverse by composing functions.