※ 引述《ian5j6 (Persistent Effort)》之銘言：
: Give an example of functions f and g , both continuous at x=0 , for which the
: composite f。g is discontinuous at x=0.
推 ILzi:f(x)= 1/(x+1) , g(x)=x-1 125.233.9.20 10/02 16:32
→ ian5j6:請問一下這個有沒有違反什麼定理?? 140.115.216.51 10/02 18:48
→ ian5j6:謝謝 140.115.216.51 10/02 18:48
這樣不行吧 , f。g 在 x = 0 根本沒有定義 ?
考慮 ,
f(x) = 0 , 當 x < 1 ; f(x) = 1 , 當 x ≧ 1
g(x) = x + 1
=> f 和 g 在 x = 0 皆連續
f。g(0) = f(g(0)) = f(1) = 1
但 lim f。g(x) = 0 ≠ f。g(0)
x→0-
=> f。g 在 x = 0 不連續
有錯請指教
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