If f (k) = k / (1 - k), then f (1 / k) f (-k) = ?

👨🏻‍🏫 學術台數學

用戶121134

2008-01-19 9:37 pm

回答 (2)

A.T.

2008-01-19 9:46 pm

✔ 最佳答案

= [ (1/k) / (1-1/k) ] x [ -k/(1+k) ]

= 1 / [ k(1-1/k) ] x [ -k/(1+k) ]

= 1/(k-1) x -k/(1+k)

= -k / (k-1)(k+1)

= -k / k^2 -1

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芸菁

2008-01-19 9:51 pm

f (1 / k)
= (1 / k) / ( 1 - 1 / k)
= 1 / (k - 1)
f (-k)
= -k / (1 + k)
∴ f (1 / k) x f (-k)
= -k / (1 + k) x 1 / (k - 1)
= k / ((1 - k) (1 + k))

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