Question

f(x)是偶函数,g(x)是奇函数,且f(x)+g(x)+f(x)g(x)=x^3+x^2+2x+1求f(x),g(x)

Answer 1

因为f(x)为偶函数,所以f(x)<>-1,则有

g(x)(1+f(x))+f(x)=x^3+x^2+2x+1

即g(x)=((x^3+x^2+2x+1)-f(x))/(1+f(x)) (1式)

则有g(-x)=((-x^3+x^2-2x+1)-f(-x))/(1+f(-x))=((-x^3+x^2-2x+1)-f(x))/(1+f(x))

又因为g(x)为奇函...