a store is offering a discount of 30% on a suit. There is a sales tax of 6%.
A) using a composition of function, represent this situatio in which the discount is taken before the sales tax is applied. the answer is (1.06)(.7x) = .742x
B) using a composition of functions represent the situation in which the sales tax is applied before the discount is taken.the answer is (1.06x)(.7) = .742x
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.
i don't understand c can you help?
Sure! Let's break down the explanation for part C.
In part A, the composition of functions is (1.06)(0.7x) = 0.742x. This means that the original price of the suit (x) is first multiplied by 0.7 to apply the 30% discount, and then the sales tax of 6% is applied by multiplying the discounted price by 1.06.
In part B, the composition of functions is (1.06x)(0.7) = 0.742x. This means that the original price of the suit (x) is first multiplied by 1.06 to apply the sales tax of 6%, and then the 30% discount is applied by multiplying the taxed price by 0.7.
Now, comparing the results of both compositions, we can see that they are equal, resulting in 0.742x for both cases. Therefore, there is no difference in the final cost between applying the discount before or after the sales tax. The order in which the operations are performed does not affect the final outcome.
This is because multiplication is an associative operation, meaning that the order in which the multiplication is done does not change the result. So, whether we multiply the discount before the sales tax or vice versa, we still end up with the same discount amount and final price.
To summarize, both compositions result in the same final cost, so it does not matter whether the discount is taken before or after the sales tax.