Question

奇偶函数习题f(x)是偶函数 g(x)是奇函数f(x)+g(x)=1/(x-1)求f(x)

Answer 1

f(x)+g(x)=1/(x-1)(1)

f(x)=f(-x)

g(-x)=-g(x),

f(-x)+g(-x)=-1/(x+1)

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)