Question

高一数学题~~

设f(x)是偶函数,g(x)是奇函数,且f(x)+g(x)=x-1分之1,求函数f(x)和g(x)的解析式.
各位大哥大姐帮忙啊

Answer 1

f(x)+g(x)=1/(x-1)......(1)
f(x)=f(-x).....偶函数得.
g(-x)=-g(x), ..........奇函数得

又有:f(-x)+g(-x)=1/(-x-1)
即:f(x)-g(x)=-1/(x+1)........(2)
(1)+(2)
f(x)=1/2*(1/(x-1)-1/(x+1))=1/(x^-1)
g(x)=x/(x^2-1)