Question

Certain superstores will often prove match or even beat a competitors price by 10%. The function g(x)= 0.90x represents the sale price of a prince 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 1

The given information is:

- The function that represents the sales price at the superstore is:

$g(x)=0.90x$

- The function that represents the HST owed on a purchase with a selling price of x dollars is:

$f(x)=0.13x$

a. The function that represents the HST owed on an item with a price tag of x dollars after it has been beaten by 10% is given by the composite function:

$h(x)=f(g(x))$

So, we replace the x in the f(x) function with the g(x) value, as follows:

$\begin{gathered} f(g(x))=0.13(0.90x) \\ h(x)=0.117x \end{gathered}$

The equation is above.

b. How much HST would be charged on a $39.99 purchase if this price is also lowered by 10% first?

Then, by using the equation we found in part a, we replace x by 39.99 and solve:

$\begin{gathered} h(x)=0.117*39.99 \\ h(x)=4.68 \end{gathered}$

$4.68 would be charged