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Math Help - Using composition of functions to determine discounts and sales tax of a product

  1. #1
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    Using composition of functions to determine discounts and sales tax of a product

    Here is a question using a composition of functions to determine discounts and sales tax of a product. Now, I probably know how to determine this without having to apply composition of functions, but I'm a little stuck on applying them to this problem.


    A store is offering a discount of 30% on a suit. There is a sales tax of 6%.

    a. Using a composition of functions, represent the situation in which the discount is taken before the sales tax is applied.

    b. Using a composition of functions, represent the situation in which the sales tax is applied before the discount is taken.

    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!
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  2. #2
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    Quote Originally Posted by qcom View Post
    Here is a question using a composition of functions to determine discounts and sales tax of a product. Now, I probably know how to determine this without having to apply composition of functions, but I'm a little stuck on applying them to this problem.


    A store is offering a discount of 30% on a suit. There is a sales tax of 6%.

    a. Using a composition of functions, represent the situation in which the discount is taken before the sales tax is applied.
    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 price with the sales tax added, rather than just the sales tax itself, then g(x)= x+ .06x= 1.06 x.)

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

    [/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]
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