An interior designer wants to decorate a newly constructed house. The function f(c) - 49x^2 - 200 represents the amount of money he earns per room decorated, where xrepresents the number of rooms he designs. The function g(x) = 1/7x represents the number of rooms the Interior designer decorates, where x is the number of hours he works.Part A: Determine the amount of money the Interior designer will make decorating the house as a function of hours he works.Part B: If the newly constructed house requires 50 hours of work, how much will the interior designer earn? Show all necessary calculations. Part C: Determine an expression to represent the difference quotient for the function found in Part A. Show all necessary work.

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BrankoI64409 BrankoI64409 · Answer 1 · 2022-10-30T15:53:39+01:00

Part A:

to find the amount of money the interior designer will make as a function of hours we need to find f(g(x)), so:

[tex]\begin{gathered} g(x)=\frac{1}{7}x \\ f(g(x))=49(\frac{1}{7}x)^2-200 \\ f(g(x))=49(\frac{1}{49}x^2)-200 \\ f(g(x))=x^2-200 \end{gathered}[/tex]

so the answer is: x^2-200

Part B:

we can use the equation we just found, so x is the number of hours so x=50 and we need to find f(g(x))

[tex]50^2-200=2300[/tex]

so the answer is: 2300