Mark works forty hours a week at a clothing store. His weekly salary is $220, plus he receives a 5% commission on sales over $1,000. Given the functions f ( x ) = 0.05 x and g ( x ) = x - 1,000, which of two compositions, ( f o g )( x ) or ( g o f )( x ), represents Mark's commission?
A) ( f o g )( x )
B) ( g o f )( x )

Question

Quizplus · Accepted Answer

To find Mark's commission, we need to first determine if his sales for the week are over $1,000. We can represent this with the function g(x) = x - 1,000, where x represents his total sales for the week.

If Mark's sales are over $1,000, then his commission is calculated as 5% of the amount over $1,000. This can be represented with the function f(x) = 0.05x.

Therefore, to find Mark's commission, we need to first use the function g(x) to determine if his sales are over $1,000, and then use the function f(x) to calculate his commission. This is represented by the composition (f o g)(x), which means "apply g first, then apply f to the result."

On the other hand, (g o f)(x) means "apply f first, then apply g to the result." This composition does not make sense in the context of the problem, because we cannot use the function f(x) to determine if Mark's sales are over $1,000.

Mark Works Forty Hours a Week at a Clothing Store