SOLUTION: 9) Certain superstores will often price match or even beat a competitor’s price by 10%. The function g(x)=0.90x represents the sale price of a piece of merchandise at such a sup

Question 1183708: 9) Certain superstores will often price match or even beat a competitor’s
price by 10%. The function g(x)=0.90x represents the sale price of a piece of merchandise at such a superstore. The function f (x)= 0.13x represents the HST
owed on a purchase with a selling price of x dollars.
a. Write a function that represents the HST owed on an item with a price tag
of x dollars after it has been beaten by 10%.
b. How much HST would be charged on a $39.99 purchase if this price is
also lowered by 10% first?
Answer by CPhill(1959) (Show Source): You can put this solution on YOUR website!
Here's how to solve this problem:
**a. Function for HST after price reduction:**
We need to find the HST owed on the *sale price* of the item. The sale price is given by g(x) = 0.90x. The HST on a price of x dollars is given by f(x) = 0.13x. We want the HST on the sale price, so we need to find f(g(x)). This is a *composition of functions*.
f(g(x)) = f(0.90x) = 0.13 * (0.90x) = 0.117x
So, the function that represents the HST owed on an item with a price tag of x dollars after it has been reduced by 10% is h(x) = 0.117x.
**b. HST on a $39.99 purchase:**
We have x = $39.99. We need to find h(39.99):
h(39.99) = 0.117 * 39.99 = 4.67883
Rounding to the nearest cent, the HST charged would be $4.68.

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