Question

Hello! Need a little help on parts A, B, and C. Thank you!

Answer 1

Given that:

- The function that represents the amount of money he earns per room decorated:

`f(x)=25x^2-100`

You know that "x" represents the number of rooms the interior designer designs.

- The function that represents the number of rooms he decorates:

`g(x)=(1)/(5)x`

You know that "x" represents the number of hours he works.

Part A

You need to substitute the function g(x) into the first function and then simplify, in order to determine the amount of money the designer will make decorating a house as a function of the hours he works.

Then, you get:

`f(g(x))=25((1)/(5)x)^2-100`
`f(g(x))=(25\cdot1^2)/(5^2)x^2-100`
`f(g(x))=(25)/(25)x^2-100`
`f(g(x))=x^2-100`

Part B

In order to determine the amount of money he will earn working 40 hours, you need to substitute this value into the function found in Part A, and then evaluate:

`x=40`

You get:

`f(g(40))=(40)^2-100`
`f(g(40))=1500`

Part C

By definition the Difference Quotient Formula is: