The function `f(x)=(x+1)/(x^3+1)` can be written as the sum of an even function `g(x)` and an odd function `h(x)` . Then the value of `|g(0)|` is___________

Answer

0

Explanation

`g(x)=(f(x)+f(-x))/(2)`
`=(1)/(2)[(x+1)/(x^(3)+1)+(1-x)/(1-x^(3))]`
`=(1)/(2)[(1)/(x^(2)-x+1)+(1)/(1+x+x^(2))]`
`=(1)/(2)[(2(x^(2)+1))/((x^(2)+1)^(2)-x^(2))]`
`=(x^(2)+1)/(x^(4)+x^(2)+1)`
` :. g(0)=1`