f(x)是奇函数,g(x)是偶函数,且f(x)+g(x)=1/(x-1) 求 f(x) g(x)

题目

f(x)是奇函数,g(x)是偶函数,且f(x)+g(x)=1/(x-1) 求 f(x) g(x)

答案

因为f(x)+g(x)=1/(x-1) (1) 所以x用-x代换掉,则f(-x)+g(-x)=-1/(x+1) 因为f(x)是奇函数,g(x)是偶函数则f(-x)+g(-x)=-1/(x+1)可化为-f(x)+g(x)=-1/(x+1) (2)[(1)+(2)]/2,可得g(x)=1/(x^2-1)[(1)-(2)]/2,可得f(x)=x/(x...