有幾條maths 唔識幫手

2007-10-22 6:29 am

１．IF f(g(x))=(x-1)over(x+3) and f(x)=2x-1 find g(x)

２.given quadratic equation(E):３Ｘ＾２＋１２Ｘ＋７＋Ｋ（（Ｘ＾２）－１）＝０
where k not equal -3
a)Find the discriminant of(E) in terms of k
b)Show that the quadratic equation (E) must have real roots for k not equal-3

４.Given that the graph of ｙ＝ａｘ＾２－８ｘ＋７passes through(1,2) where a is a constant ......（already prove that a=3）
b) Does the graph of　ｙ＝ａｘ＾２－８ｘ＋７　intersect the x-axis? Explain your answer.

回答 (1)

用戶195274

2007-10-22 8:19 am

✔ 最佳答案

1. f(g(x))=(x-1)/(x+3) and f(x)=2x-1 find g(x)
f(g(x)) = 2g(x) - 1 = (x-1)/(x+3)
2g(x) = (x-1)/(x+3) + 1
2g(x) = (x-1+x+3)/(x+3)
2g(x) = 2(x+1)/(x+3)
g(x) = (x+1)/(x+3)

2. (a) 3x^2 + 12x+7+k(x^2 - 1) = 0
(3+k)x^2 + 12x + (7-k) = 0
Discriminant = 12^2 - 4(3+k)(7-k)
= 144 - (84+16k-4k^2)
= 4k^2 - 16k + 60
(b) Discriminant = 4(k^2 - 4k + 15)
=4[k^2 - 4k + 4 + 11]
=4[(k-2)^2 + 11]
>0 for all k not equal to 3.
Therefore, (E) must have two distinct real roots.

4. (b) When a = 3, y = 3x^2 - 8x + 7
Consider the equation 3x^2 - 8x + 7=0
Discriminant = (-8)^2 - 4(3)(7) = 64-84 = -20<0
There are no real roots in the equation.
Hence, the graph would not intersect the x-axis

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有幾條maths 唔識 幫手

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有幾條maths 唔識幫手