Suppose also that you were not told the details of those separate charges, but only that the function C(n) = 1.25(55n + 300) gives total cost of the event as a function of the number of people attending.

a. Looking at the rule for C(n) what would you suspect to be:

i. the cost for party room rental?

ii. the cost per person for food and drinks?

iii. the percent rate of the service charge?

b. What function P(n) probably gives party costs for room rental, food, and drinks for n guests(before the service charge is applied)?

c. What function C(P) probably shows how to calculate total party cost, including service charge, as a function of P, the bill for room rental, food, and drinks?

d. What is the rule for C(n) = C(P(n))?

For each of the following functions f(x), give rules for two functions g(x) and h(x) so that f(x) = g(h(x)). Do not use the simple choices such as h(x) = x and g(x) = f(x). There are several other possible combinations of functions in each case.

e. f(x) = 5x – 8 f. f(x) = (2x + 5)2

3-5xf(x) h) 3

5 f(x) )

xg

Find simplest possible algebraic rules for each of the composite functions in Parts a–d. State anyrestrictions on the domains of the composite functions.

a. If f(x) = x + 4 and g(x) = x – 4, what are the rules for f(g(x)) and g(f(x))?

b. If f(x) = 5x + 2 and g(x) = 0.2x – 1, what are the rules for f(g(x)) and g(f(x))?

Find simplest possible algebraic rules for each of the composite functions in Parts a–d. State any restrictions on the domains of the composite functions.

g(f(x)). and f(g(x))for rules

theare what ,x

2-5x g(x) and

5

2f(x) If d)

g(f(x)). and f(g(x))for rules

theare what ,1-x g(x) and 1xf(x) If . 2

x

c