幾條數諗唔明...請指教－ppi93gk88d的部落格

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幾條數諗唔明...請指教

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http://i26.photobucket.com/albums/c131/km0519/42.jpg http://i26.photobucket.com/albums/c131/km0519/50.jpg http://i26.photobucket.com/albums/c131/km0519/56.jpg 42.)答案係F 50.)J<<<完全唔識 56.)H<<<完全唔識 57.)A<<<<唔明點解唔係負8

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42) |x|^2 + 2|x| - 3 = 0 (|x|+3)(|x|-1) = 0 |x| = -3 or |x| = 1 Because |x| >= 0 so |x| = -3 is rejected |x| = 1 x = +1 or -1 So the answer is F ~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~ 50) The line "y coordinate is 1 less than the square of x coordinate" means y = x^2-1 So it's a quadratic curve with y-intercept at -1 (when x = 0, y = 0^2-1 = -1) It's symmetric both side as a^2 = (-a)^2 for all positive a So the answer is J You can see on the graph, the 5 points are For x = -4, y = (-4)^2-1 = 15 For x = -1, y = (-1)^2-1 = 0 For x = 0, y = 0^2-1 = -1 For x = 2, y = 2^2-1 = 3 For x = 4, y = 4^2-1 = 15 ~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~ 56) (sqrt(1-cos^2x))/sin x + (sqrt(1-sin^2x))/cos x = sqrt(sin^2x))/sin x + sqrt(cos^2x)/cos x (because cos^2x + sin^2x = 1) = sin x/sin x + cos x/ cos x = 1 + 1 = 2 So the answer is H ~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~ 57) For f(x) = sqrt(x) For g(x) = 7x+b It passes through (4,6) so we consider when x = 4. g(4) = 7*4+b = 28+b So if f(g(x)) passes through (4,6) y = f(g(x)) y = f(7x+b) y = sqrt(7x+b) If it passes through (4,6) 6 = sqrt(7*4+b) 6^2 = 7*4+b 36 = 28+b b = 8 So the answer is A 2006-11-09 12:20:38 補充：小小提示：26) |x| = -3 不用考慮因為所有 |x| 都大過或等如 050) 先把題目轉換到 equation 就會較易明白「y coordinate is 1 less than the square of x coordinate」即是 y 是 x 二次方 - 1 所以可以用 y = x^2-1 表示。 2006-11-09 12:25:24 補充： 56) 只要用 cos^2x + sin^2x = 1 這公式就可以簡化：1-sin^2x = cos^2x 和1-cos^2x = sin^2x57) 首先要1. 將 y = f(g(x)) 轉換到 y = f(7x+b) [因為 g(x) = 7x+b]2. 將 y = f(7x+b) 轉換到 y = sqrt(7x+b) [因為 f(X) = sqrt(X) 但今次要考慮 X=7x+b]3. 再將 (4,6) 這個通過的點代入 y = sqrt(7x+b) 裡面。

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