# Thread: Composition function word problem

1. ## Composition function word problem

Hi,

I hope someone can help. I'm trying to answer the following question:

So to summarize the question, I'm suppose to develop a function which expresses this discount cost in terms of the number of people attending.

According to the textbook, this function would be:

The issue is, is that I don't fully understand how this function matches what we're looking for in this question. I say this because it appears that this solution above expresses the banquet cost which incorporates the discount cost, rather than what the question is asking for, which is to exclusively find the discount cost for the number of people attending. I thought that the right way to represent the discount cost for the number of people attending would be, D(p) = 31.96p, since this function just considers the discount in terms of the number of people. Can someone please explain to me whether or not my thinking is wrong about this?

2. ## Re: Composition function word problem

$B(p) = 975+39.95p$
$D(B) = (100\%-20\%)B$

$D(p) := D(B(p)) = (0.8)(975+39.95p) = 780+31.96p$

3. ## Re: Composition function word problem

Originally Posted by SlipEternal
$B(p) = 975+39.95p$
$D(B) = (100\%-20\%)B$

$D(p) := D(B(p)) = (0.8)(975+39.95p) = 780+31.96p$
Wouldn't D(p), which you wrote above, represent the total banquet cost which incorporates the 20% discount, rather than the number of people attending?

4. ## Re: Composition function word problem

Originally Posted by otownsend
Wouldn't D(p), which you wrote above, represent the total banquet cost which incorporates the 20% discount, rather than the number of people attending?
A function takes an input and gives an output. The function $B$ is a function of the number of people attending that yields the total bill for that banquet. Its input is the number of people. Its output is the total bill. You are asked to create a Discount function that yields the discounted price (which is described as a discount off the total bill). So, the original discount function takes a total bill, or $B$, and yields the discounted price. They want another Discount function that takes the number of people and gives the total discounted price. But, it is not giving the price per person. It is giving the total discounted price.

5. ## Re: Composition function word problem

Makes sense. Thank you!