Question

James and Aiesha are planning a wedding reception at the Grand Ballroom of the Marriott. It costs then a base fee of $2,000 plus $50 per guest. If their budget for the Grand Ballroom expenses is limited to $10,000.

State the cost as a function of number of guests.





Determine the expression for the inverse.





State the domain for this situation.





State the range for this situation.

Answer 1

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

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.