Problem 1 given that f x 5x - 7 and g x 5 - x2

Question

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.

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))