You work forty hours a week at a furniture store. You receive a 1,200 dollar weekly salary, plus a 4.1% commision on sales over 12,000 dollars. Assume that you sell enough this week to get the commission. Given the functions f (x) = 0.041x and g (x) = x ̆12,000, which of (fog) (x) and (gof) (x) represents your commission?

Question

Mathematics

Emelia Brady

14 March, 03:32

You work forty hours a week at a furniture store. You receive a 1,200 dollar weekly salary, plus a 4.1% commision on sales over 12,000 dollars. Assume that you sell enough this week to get the commission. Given the functions f (x) = 0.041x and g (x) = x ̆12,000, which of (fog) (x) and (gof) (x) represents your commission?

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Answers (1)

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Franklin Stevenson · Answer 1

If you call x the total value of the sales, the sale over 12,000 will be: g (x) = 12,000 - x.

And the commission is 4.1% of that = 0.041 * (12,000 - x) = 0.041 * g (x)

So, if f (x) = 0.041x, to calculate the commission you first have to calculate g (x) = 12,000 - x, and the f (g (x)) = 0.041[12,000 - x].

Which leads you to the solution for the commission as [f o g] (x) = f (g (x)) = 0.041 (12,000 - x).

Answer: [ f o g] (x)