Question 952010
A catering service uses the function
 [c(x) = (300 + 17x)/x] to determine the amount, in dollars, it charges per person for a sit-down dinner, where x is the number of people in attendance.
 (a) Find c(75) and explain what it represents.
c(75) = (300+17*75)/75 = $21
 The company charges $21 per person to cater a dinner for 75 people.
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 (b) Find c^−1.
 Interchange x and y to get::
(300 + 17*y)/y = x
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Solve for y to get :
300+17*c(x) = x*c(x)
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300 + 17y = yx
17y-yx = -300
y(x-17) = 300
y = 300/(x-17)
That is c^-1:::
y is # of people
x is cost per person
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(c) Use c^−1 to determine how many people attended a dinner for which the cost per person was $19.00.
 Solve::
y = 300/(x = 17)
y = 300/(19-17)
y = 300/2
y = 150 people
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Cheers,
Stan H.
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