Respuesta :
Answer:
1) The cost function, f(x) = 10,000 + x × 50
2) The expression for the inverse of the cost function is y = x/50 - 200
3) The domain is 10,000, 10,050, 10,100, ... . x ∈ 10,000+(n - 1)×50
4) The range is the set of whole numbers, W. y ∈ W
Step-by-step explanation:
The given information are;
The base fee for the Grand Ballroom = $2,000
The fee per guest = $50
The limit of their budget for the Grand Ballroom = $10,000
1) The cost function, f(x), for the number of guests, x is given as follows;
f(x) = 10,000 + x × 50
2) The expression for the inverse of the cost function is given as follows;
Let f(x) = y, we have;
y = 10,000 + x × 50
Therefore;
y - 10,000 = x × 50
x = (y - 10,000)/(50)
Interchanging the variables a and y in the above equation, gives;
y = (x - 10,000)/(50) = x/50 - 200
The inverse of the function is therefore, y = x/50 - 200
3) The domain is the set of possible input values to x which is given as follows;
The value y in the situation of the inverse = The number of guests, which is the set of whole numbers
Therefore, the domain, consists of the following numbers;
10,000, 10,050, 10,100, ... , 10,000+(n - 1)×50
Where;
n = The set of real numbers
4) The range is the set of whole numbers, W.
