Question

Suppose you are paid an annual salary, plus a bonus of 20% on annual sales over $500,000. Consider the two functions f(x) = x − 500,000 and g(x) = 0.2x where x equals your annual sales. Which function composition gives the bonus amount when your sales are over $500,000?

A) x(f(g))

B) x(g(f))

C) g(f(x))

D) f(g(x))

Answer 1

C.
`g\,\circ \, f (x) =g(f(x))`

Explanation:

Let be
`f(x) = x-500000` the excedent on annual sales and
`g(x) = 0.2\cdot x` the bonus factor, to determine the bonus amount a composition of
`f(x)` is
`g(x)` must be done. That is:

`g\,\circ \, f (x) =g(f(x))`

Hence, the right answer is C.