Final answer:
Option (a) g(f(x)) = 0.05(x-3000), appears to be the most typical bonus structure, providing a 5% bonus on the amount by which x exceeds 3000.
Step-by-step explanation:
The task given is to provide and describe a function composition that can be used to determine the weekly bonus. Based on the options provided:
- (a) g(f(x)) = 0.05(x-3000) would give us a bonus that's 5% of the amount by which x exceeds 3000, effectively making 3000 a threshold before the bonus applies.
- (b) f(g(x)) = 0.05x - 3000 would suggest subtracting 3000 after computing 5% of x, which isn't typical for a bonus structure.
- (c) f(g(x)) = 0.05(x-3000) is similar to option a, and would again represent a 5% bonus of the amount over 3000.
- (d) g(f(x)) = 0.05x - 3000, like option b, also doesn't seem to structure the bonus in a typical way.
Option (a) seems to be the most reasonable representation of a typical bonus structure, where a base threshold must be exceeded before the bonus percentage is applied.