Problem 1: Given that f (x) = 5x - 7 and g (x) = 5 - x2, calculate
a. f (g)(0))
b. g (f)(0))
Problem 2: Use the table of values to evaluate the expressions below.
X
|
f(x)
|
g(x)
|
0
|
4
|
8
|
1
|
9
|
6
|
2
|
2
|
5
|
3
|
0
|
7
|
4
|
3
|
2
|
5
|
5
|
4
|
6
|
8
|
3
|
7
|
6
|
1
|
8
|
7
|
9
|
9
|
1
|
0
|
a. f(g)(8))
b. g(f)(3))
c. f(f)(9))
d. g(g)(0))
Problem 3:
Use the graph to evaluate the expressions below.
![1276_evaluate the expressions .jpg](https://secure.tutorsglobe.com/CMSImages/1276_evaluate%20the%20expressions%20.jpg)
a. f(g)(5))
b. g(f)(1))
c. f(f)(0))
d. g(g)(3))
Problem 4: Let f(x) = 1/x - 5 and g(x) 4/x + 5.
Find the following functions. Simplify your answer.
a. f(g)(x))
b. g(f)(x))
Problem 6: If f(x) = x4 + 6, g(x) = x - 6 and h(x) = √x, then
f(g(h(x)))
Problem 7: The number of bacteria in a refrigerated food product is given by N(T) = 29T2 - 115T + 91, 3
When the food is removed from the refrigerator, the temperature is given by T(t) = 9t + 1.3. where t is the time in hours.
Find the composite function N(T)(t)):
N(T(t))
Find the time when the bacteria count reaches 26365. Give your answer accurate to at decimal places.
Problem 8: The function h(x) = (x + 9)3 can be expressed in the form f(g(x)) where f(x) = x3, and g(x) is defined below:
g(x) = ?
Problem 9: The function D(p) gives the number of items that will be demanded when the price is p. the production cost, C(x) is the cost of producing x items. To determine the cost of production when the price is $8, you would:
Evaluate c(D(8))
Solve C(D(p)) = 8
Solve D(C(x)) = 8
Evaluate D(C(8))