Question

设f(x)为奇函数,g(x)为偶函数,且f(x)+g(x)=1/x-1,则f(x)=

Answer 1

f(x)+g(x)=1/(x-1) ①

则f(-x)+g(-x)=1/(-x-1) ②

f(x)是奇函数,g(x)是偶数,则：f(-x)=-f(x),g(-x)=g(x)

所以②式化为：-f(x)+g(x)=-1/(x+1) ③

①-③得：2f(x)=1/(x-1)+1/(x+1)

2f(x)=2x/(x²-1)

所以：f(x)=x/(x²-1)