Given $f(x)=x^{3}+1$ and $g(x)=x-1$, simplify the function operation $f(x)-g(x)$. $x^{3}-x$ $-x^{3}+2$ $x^{3}-x+2$ $x^{4}+1$

Step 1 ：Given functions $f(x)=x^{3}+1$ and $g(x)=x-1$

Step 2 ：The operation $f(x)-g(x)$ means that we subtract the function $g(x)$ from the function $f(x)$

Step 3 ：This is done by subtracting the corresponding terms of the functions

Step 4 ：Subtract $x-1$ from $x^{3}+1$

Step 5 ：Subtract $x$ from $x^{3}$ and $-1$ from $1$

Step 6 ：The simplified form of the function operation $f(x)-g(x)$ is $x^{3}-x+2$

Step 7 ：Final Answer: \(\boxed{x^{3}-x+2}\)