Question

The regular price of a pair of jeans is x dollars. Let f(x) = x − 15, where f represents the price of the jeans discounted by $15. Let g(x) = 0.8timesx represent the price of the jeans discounted by 20%. Use composition to find the price of the jeans if they are first discounted by 20%, then by $15.

Answer 1

@satellite73

Answer 2

Given two functions, f(x) and g(x) we can form two composites: (fog)(x) or (gof)(x).
Which ones to choose for this problem?
(fog)(x) = f(g(x)). The innermost function, g(x), is calculated first.
(gof)(x) = g(f(x)). The innermost function, f(x), is calculated first.

What does the problem state is calculated first?

Answer 3

Well wouldnt it be (gof)(x) = g(f(x)). The innermost function, f(x), is calculated first.

Answer 4

The problem at the end says: "first discounted by 20%, then by $15"
f(x) represents discount by $15.
g(x) represents discount by 20%
First discounted by 20% implies g(x) is done first and so g(x) should be the innermost function.

Answer 5

Because youi have to apply the 20% first?

Answer 6

Yes. The problem says apply 20% first and since the problem says g(x) is the 20% discount function, g(x) must be the innermost function and f(x) the outer function. So we need to find (fog)(x) or f(g(x))
f(x) = x - 15
(f o g)(x) = f(g(x)) = g(x) - 15 = 0.8x - 15

Answer 7

so what would you start with to find said part

Answer 8

Not sure what you are asking. The problem has been solved in my previous reply.

Answer 9

(f o g)(x) = 0.8x - 15
The first choice is the correct answer.

Answer 10

As I thought t-t i asked this question a while ago buht no one answered :c

Answer 11

Is the solution clear or do you have some questions?

Answer 12

thank you but that was all :P Thank you for your help again

Answer 13

You are welcome.