Question

The function $f\left(x\right)=\frac{x+1}{x^3+1}$ can be written as the sum of an even function $g\left(x\right)$ and an odd function $h\left(x\right)$. Then the value of $|g\left(0\right)|$ is

Answer 1

$g\left(x\right)=\frac{f\left(x\right)+f(-x)}{2}$
$=\frac{1}{2}[\frac{x+1}{x^3+1}+\frac{1-x}{1-x^3}]$
$\Rightarrow g\left(0\right)=1$