S4 Maths ( f(x) )

[匿名]

2012-08-23 8:11 pm

4. Consider the function f(x) = (x-3)(x+1)-(x-2)(x+2)

a) Determine the type of function f(x).

b) Find the x-intercept(s) and y-intercept of the graph of y=f(x).

9.It is given that g(x) = a(x-1)(x+1) - b(x +1)^2 ,g(1) = 4 and g(0) = -3

a) Find the values of a and b.

b) Factorize g(x).

c) Hence, solve g(x) = 0.

回答 (1)

用戶2053

2012-08-24 7:48 am

✔ 最佳答案

4a)f(x) = (x - 3)(x + 1) - (x - 2)(x + 2) = (x² - 2x - 3) - (x² - 4) = - 2x + 1.
∴ f(x) is a linear function.
b)y = f(x)
y = - 2x + 1
2x + y = 1
x / (1/2) + y / (1) = 1 ............. (Intercept form : x/a + y/b = 1)
∴ x - intercept = 1/2 , y - intercept = 1. 9a) g(x) = a(x - 1)(x + 1) - b(x + 1)²g(1) = 4
a(1 - 1)(1 + 1) - b(1 + 1)² = 4
0 - 4b = 4
b = - 1g(0) = - 3
a(0 - 1)(0 + 1) - b(0 + 1)² = - 3
- a - b = - 3
- a - (-1) = - 3
a = 4
b)Substitute a = 4 and b = - 1 into g(x) :g(x) = 4(x - 1)(x + 1) - (- 1)(x + 1)²
g(x) = (x + 1) [ 4(x - 1) + (x + 1) ]
g(x) = (x + 1) (5x - 3)
c)g(x) = 0
(x + 1) (5x - 3) = 0
x + 1 = 0 or 5x - 3 = 0
x = - 1 or x = 3/5

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