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Yahoo!奇摩知識+ - 分類問答 - 科學常識 - 已解決
Yahoo!奇摩知識+ - 分類問答 - 科學常識 - 已解決 
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幫我解下列數學題目(20點
Sep 15th 2013, 13:58

f(x)=x^2+x
g(x)=2/(x+3)

1. (f-g)(2)
(f-g)(x) = f(x) - g(x) = x^2+x - 2/(x+3)
(f-g)(2) = 2^2 + 2 - 2/5 = 28/5

2. (f/g)(1)
(f/g)(x) = (x^2+x)/[2/(x+3)]
(f/g)(1) = 2/(1/2) = 4

3. g^2(3)
g^2(x) = [2/(x+3)]^2
g^2(3) = (2/6)^2 = 1/9

4. (f。g)(1)
(f○g)(x) = f(g(x)) = g^2(x)+g(x) = [2/(x+3)]^2 + 2/(x+3)
(f○g)(1) = 1/4 + 1/2 = 3/4

5. (g。f)(1)
(g。f)(x) = g(f(x)) = 2/(f(x)+3) = 2/(x^2+x+3)
(g。f)(1) = 2/5

6. (g。g)(3)
(g。g)(x) = g(g(x)) = 2/(2/(x+3)+3)
(g。g)(3) = 2/(2/(3+3)+3) = 2/(1/3 + 3) = 2/(10/3) = 6/10 = 3/5

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