20點******急!!!!!!!!!數學Number and Algebra!!!!!come in!!!*****

2008-10-08 5:36 am

1 . It is given that f(x)=3x-2 .
(a).Find the values of f(2) and f(4) .
(b).Verify that [f(2)]²≠f(2²) .

2.It is given that f(x)=(x+3)(x+2)-k²and f(k)=2k .
(a).Find the value of k .
(b).Hence,solve for x if 2x-f(x)=0 .

3.It is given that f(x)=x²-kx .
(a).Find f(x+2) and f(x-2) .
(b).If f(x+2)-f(x-2)=kx-32 , find the value of k .
(c).Hence , solve for x if f(x+2)=f(x-2)+40 .

4.It is known that the function F(n)=500+4n represents the cost(in dollars) for holding a party with n guests .
(a).Find the cost for holding a party with 50 guest .
(b).If the cost for holding a party is $840 ,, find the number of guests .
(c).If each guest has to pay $10 ,
(i).write a function H(n) to express the profit(in dollars) for holding a party with n guest .
(ii).find the profit when there are 150 guest .

回答 (1)

Uncle Michael

2008-10-08 6:24 am

✔ 最佳答案

1.
f(x) = 3x - 2 .

(a).
f(2)
= 3(2) - 2
= 4

f(4)
= 3(4) - 2
= 10

(b).
[f(2)]2
= [4]2
= 16

f(22)
= f(4)
= 10

Hence, [f(2)] ≠ f(2)

=====
2.
f(x)=(x + 3)(x + 2) - k

(a)
f(k) = 2k
(k + 3)(k + 2) - k = 2k
k2 + 5k + 6 - k2 = 2k
3k = -6
k = -2

(b).
2x - f(x) = 0
f(x) = 2x
Hence, x = -2

=====
3.
f(x)=x - kx

(a).
f(x + 2)
= (x + 2)2 - k(x + 2)
= x2 + 4x + 4 - kx - 2k
= x2 + (4 - k)x + (4 - 2k)

f(x - 2)
= (x - 2)2 - k(x - 2)
= x2 - 4x + 4 - kx + 2k
= x2 - (4 + k)x + (4 + 2k)

(b).
f(x + 2) - f(x - 2) = kx - 32
[x2 + (4 - k)x + (4 - 2k)] - [x2 - (4 + k)x + (4 + 2k)] = kx - 32
x2 + (4 - k)x + (4 - 2k) - x2 + (4 + k)x - (4 + 2k) = kx - 32
(4 - k)x + (4 - 2k) + (4 + k)x - (4 + 2k) = kx - 32
4x - kx + 4 - 2k + 4x + kx - 4 - 2k = kx - 32
8x - kx + 32 - 4k = 0
(8 - k)x + 4(8 - k) = 0
(8 - k)(x + 4) = 0
k = 8 ooro x = -4 (rejected)

(c).
From (b):
f(x + 2) - f(x - 2) = 8x - 32

f(x + 2) = f(x - 2) + 40
f(x + 2) - f(x - 2) = 40
8x - 32 = 40
8x = 72
x = 9

=====
4.
t is known that the function F(n)=500+4n represents the cost(in dollars) for holding a party with n guests .
(a).
Cost of the party
= $[500 + 4(50)]
= $700

(b).
500 + 4n = 840
4n = 340
n = 85
Number of guest = 85

c.(i).
H(n) = 10n - (500 + 4n)
H(n) = 10n - 500 - 4n
H(n) = 6n - 500

c.(ii).
Profit
= $(6n - 500)
= $[6(150) - 500]
= $400
=

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