Answer:
The composition of the functions is g(f(x))
Step-by-step explanation:
* Lets revise what is the meaning of composite functions
- A composite function is created when one function is substituted into
another function
- Ex: f(g(x)) is the composite function formed when g(x) is substituted for
x in f(x)
* Lets solve the problem
- Sally earns a 2% commission on total sale over $5000
- Which is paid as a bonus at the end of the year
- Let her total sales be represented by x
- f(x) = x - 5000 and g(x) = 0.02 x
- We need to find the suitable composite function which represents her
bonus at the end of the year
∵ She earns a 2% commission on total sale over $5000
∵ Her total sale is $x
- At first subtract from x the $5000, then multiply the answer by 2%
- That mean she earns 2% of (x - 5000)
∵ 2% = [tex]\frac{2}{100}[/tex] = 0.02
∴ She earns 0.02(x - 5000)
- Lets find the composite functions which give us 0.02(x - 5000)
∵ f(x) = x - 5000
∵ g(x) = 0.02 x
- Substitute x in g(x) by f(x)
∴ g(f(x)) = 0.02 (x - 5000)
* The composition of the functions is g(f(x))
