1) f(x) = x2 ? 7x + 12, find f(?a), f(a ? 3), and f(a + h). 2) Find for the func
ID: 2833834 • Letter: 1
Question
1) f(x) = x2 ? 7x + 12, find f(?a), f(a ? 3), and f(a + h).
2) Find
for the function.
f(x) = ?2x2 ? 3
3)Suppose that the cost function for producing a certain item is C (n) = 2n ? 5, where n represents the number of items produced. Compute C(190), C(600), C(600), andC(1450).
C (1450)
4)A motel advertises that it will provide dinner, dancing, and drinks for $80 per couple at a New Year's Eve party. It must have a guarantee of 20 couples. Furthermore, it will agree that for each couple in excess of 20, it will reduce the price per couple for all attending by $0.25. How many couples will it take to maximize the motel's revenue?
5)Determine the indicated functional values. (If an answer is undefined, enter UNDEFINED.)
(f * g)(1)=
(g * f) (2)=
6)
If f(x) = 3|x| ? 8, and g(x) = ?|x| + 8, find f(2), f(-1), g(-5), and g(-6).
f(a + h) ? f(a) hExplanation / Answer
1.
f(-a)= (a*a) +7a +12
f(a-3)= (a*a) -13a + 42
f(a+h) = (a*a) +2ah +(h*h) -7a -7h +12
2.
[f(a+h)-f(a)]/h= [-2(a+h)^2 - 3 +2a^2 +3]/h
= - 4a - h
3.
C(190)=380-5 = 375
C(600)= 1200-5 = 1195
C(1450)= 2900- 5 = 2895
4.
let x=number of couples to maximize motel's revenue
x-20=number of couples in excess of 20
.25(x-20)=reduction in price per couple
Price per couple=[80-0.25(x-20)]
Revenue=number of couples*price per couple
y=x[80-(.25(x-20)]
=x[80-.25x+5]
=x[-.25x+85]
=-.25x^2+85x
complete the square
y=-.25(x^2-340+170^2)+.25*170^2
y=-.25(x-170)^2+7225
This is a parabola that opens downwards with a maximum of 7225 at x=170
How many couples will it take to maximize the motel's revenue=170
5.
(f o g)(x)= 8x^2 -64x +127
(f o g)(1)= 8-64+127
= 71
(g o f)(x)= 4x^2 + 6
(g o f)(1)= 22
6.
f(2)= 6-8= -2
f(-1)= 3-8 = -5
g(-5)= -5+8 = -3
g(-6)= -6+8 = 2
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