Question

You have a coupon for your favorite clothing store for $25 off any purchase of more than $50. The store is also running a 20%-off sale on its entire inventory. Let x be the original price, be the price with the $25 coupon applied, and be the price with the 20% discount applied.
A) Write an expression for f(x)
B) Write an expression for g(x)
C) What would an expression for (f o g)(x) represent
D) What would an expression for (g o f)(x) represent
E).If the store allows you to apply both the 20% discount and the $25-off coupon, does it matter which you apply first? How do you know?

Answer 1

For A and B, what do you think the expression would be?
x is the original price
f(x) is the price with the 20$ coupon applied..
so ...

Answer 2

f(x) only applies if it is greater than or equal to 50 as well, so keep that in mind.

Answer 3

25$ coupon *

Answer 4

x+25>= 50?

Answer 5

A coupon means discount. and no.

Answer 6

f(x) = x - 25, if x >= 50

Answer 7

Do you understand why?

Answer 8

Oh, so when you spend $50 or more you get a $25 discount

Answer 9

Yes.

Answer 10

good good , now try the expression for g(x)
what is 20% off in decimal terms?

Answer 11

.2

Answer 12

20% off = 0.80 of the original price
so g(x) would be then.

Answer 13

g(x)= .80x?

Answer 14

yes!

Answer 15

in terms of words what would (f o g) represent, you're applying g first and then f.

Answer 16

So I could say, (f o g)(x) represents the total price after using 20% off? I have always been horrible for the (f o g) and (g o f)

Answer 17

you're applying 20% off and then the coupon

Answer 18

So that is what I would write as my answer?

Answer 19

yes.

Answer 20

using analysis skills what then would be (g o f) ?

Answer 21

When you apply the coupon before you get the 20% discount

Answer 22

yes