Let f(x) be the function that takes regular price, x, to the discounted price. Let g(x) be the function that takes the price to the sales tax. Then, if x is the regular price, g(f(x)), the composition of f and g, is the sales tax. Now, you say you know how to determine this so you must know that the discounted price is the regular price, x, minus 30% of x: f(x)= x- .3 x= .7x. Also, if the price is x, the sales tax is g(x)= .06x. So the sales tax on the discounted price is g(f(x))= g(.7x)= .06(.7 x)= .042x.

(IF the problem was to get the pricewiththe sales tax added, rather than just the sales tax itself, then g(x)= x+ .06x= 1.06 x.)

Here, we clearly want the price with the sales tax added. This is now f(g(x)) with the g(x)= 1.06 x.b. Using a composition of functions, represent the situation in which the sales tax is applied before the discount is taken.

[/quote]c. Compare the composite functions from parts a and b. Does one of them result in a lower final cost? Explain why or why not.

Any help or advice would be greatly appreciated!!

Thanks![/QUOTE]