作者Ru83u86 (假牙)
看板Math
标题[微积] 帮忙求一微积课本题目~
时间Tue Jun 14 09:02:06 2011
f(x)=(ax+b)/(cx+d) 假设bc-ad不等於0
1.求f^-1(x) (就是反函数QQ)
2.为何要具备bc-ab不等於0的条件?
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※ 发信站: 批踢踢实业坊(ptt.cc)
◆ From: 114.44.108.168
1F：→ suhorng :题目是(ax+b)/(cx+d)? 06/14 09:05
※ 编辑: Ru83u86 来自: 114.44.108.168 (06/14 09:08)
※ 编辑: Ru83u86 来自: 114.44.108.168 (06/14 09:08)
2F：推 suhorng :当 bc-ad!=0, 设 x = (ay+b)/(cy+d) 06/14 09:09
3F：→ suhorng :=> (cx-a)y + (d-b) = 0 => y = (b-d)/(cx-a) 06/14 09:09
4F：→ Ru83u86 :太帅了~感恩 06/14 09:09
5F：→ suhorng :若 bc-ad=0 则 f(x) 是常数 反函数不存在 06/14 09:10
6F：→ Ru83u86 :f(x)=x^2+x+1 有反函数f^-1 求(f^-1)'(3) 06/14 09:11
7F：→ suhorng :(f^-1)(f(x)) = x => (f^-1)'(f(x))f'(x) = 1 06/14 09:12
8F：→ suhorng :(链锁律.) 所以 x 代 1 得 (f^-1)'(f(1))f'(1) = 1 06/14 09:13
9F：→ suhorng :=> (f^-1)'(3) * 3 = 1 => (f^-1)'(3) = 1/3 06/14 09:13
10F：→ suhorng :或是 x 代 -2 得 (f^-1)'(3) = -1/3 06/14 09:17
11F：→ suhorng :...第三行是 b-dx 才对 06/14 09:24