1. Given that f(x)=(x+2)(x-2)+ax+b. If f(2)=4 adn f(-2)=4, find the values of a and b.
2. Given that g(x)=2x-1.
(a) if h(x)=g(2x-1), find the algebraic representation of h(x).
(b) if g(p-2)=h(p), find the value of p.
F. 4 maths
2009-10-11 10:44 pm
回答 (2)
2009-10-11 10:50 pm
✔ 最佳答案
1. f(x) = (x + 2)(x - 2) + ax + bf(2) = 4
(2 + 2)(2 - 2) + 2a + b = 4
2a + b = 4 ... (1)
f(-2) = 4
(-2 + 2)(-2 - 2) + a(-2) + b = 4
-2a + b = 4 ... (2)
Solving (1) and (2), a = 0, b = 4
2.a. g(x) = 2x - 1
h(x) = g(2x - 1) = 2(2x - 1) - 1 = 4x - 3
b. g(p - 2) = h(p)
2(p - 2) - 1 = 4p - 3
2p - 5 = 4p - 3
p = -1
參考: Physics king
2009-10-18 7:02 pm
1. Put f(2)=2 into f(x)=(x+2)(x-2)+ax+b.
(2+2)(2-2)+a(2)+b = 2
2a+b=2 .....(1)
Put f(2)=4 into f(x)=(x+2)(x-2)+ax+b
(-2+2)(-2-2)+a(-2)+b = 4
-2a+b=4 .....(2)
(2)-(1),
-4a=2
a=-1/2
Put a=-1/2 into (1),
2(-1/2)+b = 2
b=3
2(a)
g(x) = 2x - 1
h(x) = g(2x - 1) = 2(2x - 1) - 1 = 4x - 3
(b)
g(p - 2) = h(p)
2(p - 2) - 1 = 4p - 3
2p - 5 = 4p - 3
-2p = 2
p = -1
收錄日期: 2021-04-19 15:29:58
原文連結 [永久失效]:
https://hk.answers.yahoo.com/question/index?qid=20091011000051KK00992