Please state the steps of " If f(x) = x / (1-x), then f(1/x) f(-x) = ? " .
Thank you very much.
If f(x) = x / (1-x), then f(1/x) f(-x) = ?
2007-11-11 10:07 pm
回答 (3)
2007-11-11 10:12 pm
✔ 最佳答案
f(1/x) = (1/x) / [1-(1/x)] = (1/x) /[(x-1)/x]= 1/(x-1)
f(-x) = -x/[1-(-x)] = -x/(1+x)
Hence f(1/x) f(-x) = 1/(x-1) * [-x/(1+x)]
= -x/(x-1)(x+1)
=-x/(x^2 - 1)
= x/(1-x^2)
2007-11-12 10:09 pm
f(1/x)f(-x) = [(1/x) / (1 - 1/x)] [(-x) / (1 - (-x))]
= (1/x) / [(x-1)/x] [-x / ( 1+x)]
= -1/[x(x-1)(x+1)]
2007-11-12 14:10:03 補充：
in the last step, it should be -x/[(x-1)(x+1)]
= (1/x) / [(x-1)/x] [-x / ( 1+x)]
= -1/[x(x-1)(x+1)]
2007-11-12 14:10:03 補充：
in the last step, it should be -x/[(x-1)(x+1)]
2007-11-11 10:52 pm
f(1/x) f(-x)=1/[x(1-x^-1)] x [(-x)/(1+x)]
=(x-1)^-1 x (-x)/(1+x)
=(-x)/(x^2-1)
=x/(1-x^2)
=(x-1)^-1 x (-x)/(1+x)
=(-x)/(x^2-1)
=x/(1-x^2)
參考: me
收錄日期: 2021-04-13 18:12:11
原文連結 [永久失效]:
https://hk.answers.yahoo.com/question/index?qid=20071111000051KK02061