Answer:
(f o g)(x) represents Dale's commission
Step-by-step explanation:
The composite function (f o g)(x) means g(x) is the domain of f
The composite function (g o f)(x) means h(x) is the domain of g
∵ f(x) = 0.05x
∵ g(x) = x - 3000
- Substitute x in f(x) by g(x) to find (f o g)(x)
∵ (f o g)(x) = f(x-3000)
∵ f(x-3000) = 0.05(x - 3000)
∴ f(x-3000) = 0.05x - 150
∴ (f o g)(x) = 0.05x - 150
- Substitute x in g(x) by f(x) to find (g o f)(x)
∵ (g o f)(x) = g(0.05x)
∵ g(0.05x) = 0.05x - 3000
∴ (g o f)(x) = 0.05x - 3000
∵ Dale's commission is 5% for sales over $3,000
∵ His sales is $x
- Subtract 3000 from x, then multiply the answer by 5%
∴ His commission = (x - 3000) × 5%
∵ 5% = [tex]\frac{5}{100}=0.05[/tex]
∴ His commission = (x - 3000) × 0.05
- Multiply each term in the bracket by 0.05
∴ His commission = 0.05(x) - 0.05(3000)
∴ His commission = 0.05x - 150
∵ (f o g)(x) = 0.05x - 150
∴ (f o g)(x) = Dali's commission
∴ (f o g)(x) represents Dale's commission
