Question

You have a coupon for your favorite clothing store for $35 off any purchase of $70 or more. The store is running a 25% off sale on its entire inventory. Let x be the original price, f(x) be the price with the coupon applied, and g(x) be the price with the discount applied.
a. Write an expression for f(x).



b. Write an expression for g(x).



c. What would the expression (f o g)(x) represent?



d. What would the expression (g o f)(x) represent?
PLEASE SHOW ALL WORK

Answer 1

f(x) = x - 35
g(x) = x- 25x/100 = x - x/4 = 3x/4

f(g(x)) = 3/4(x) -35

g(f(x)) = 3*(x-35)/4

Answer 2

So how did you figure those out? Thank you for the help

Answer 3

given x is the original price

f(x) happens when x is greater than 70
then f(x) = x-35

g(x) is on all the inventory so no matter what price is
g(x) = x -25%(x)

f(g(x)) = put x = g(x) in f(x)

g(f(x)) = put x =f(x) in g(x)

Answer 4

Okay I understand. For 3 and 4 though, what do those equations represent? Thank you!