F.4 Maths (4)

Please check question 3

2009-10-20 22:54:25 補充：
1. It is given that f(x)=2x+3
(a) Find f(2t) and f(t+2)
f(2t) = 2(2t) + 3 = 4t + 3
f(t + 2) = 2(t + 2) + 3 = 2t + 7
(b) Hence, solve the equation f(2t)=1/2f(t+2)-1
f(2t) = (1/2)f(t + 1) - 1
4t + 3 = (1/2)(2t + 7) + 1
4t + 3 = t + 4.5
3t = 1.5
t = 0.5
2. It is given that G(t)=t^2+at and G(-4)=-4
(a) Find the value of a
G(-4) = 16 - 4a = -4
4a = 20
a = 5
(b)Hence, solve the equation G(b-1)-1/3G(3)=-2
G(b - 1) - (1/3)G(3) = -2
(b - 1)^2 + 5(b - 1) - (1/3)(9 + 15) = -2
b^2 - 2b + 1 + 5b - 5 - 8 = -2
b^2 + 3b - 10 = 0
(b + 5)(b - 2) = 0
b = 2 or b = -5
3.It is given that f(x)=4-6x
(a) Find the value of f(2) and f(-2/3)
f(2) = 4 - 6(2) = -8
f(-2/3) = 4 - 6(-2/3) = 4 + 4 = 8
(b) If f(k)=-2/3 ,find the value of k.
f(k) = 4 - 6k = -2/3
4 + 2/3 = 6k
14/3 = 6k
k = 7/9