Question 1183708
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.