For $f(x)=x+1$ and $g(x)=2 x^{2}-x-3$, find $(f-g)(x)$.

Step 1 ：Given the functions $f(x)=x+1$ and $g(x)=2x^{2}-x-3

Step 2 ：We are asked to find $(f-g)(x)$, which means we need to subtract $g(x)$ from $f(x)$

Step 3 ：Subtract each term in $g(x)$ from the corresponding term in $f(x)$

Step 4 ：This gives us $-2x^{2} + 2x + 4$

Step 5 ：So, $(f-g)(x) = \boxed{-2x^2 + 2x + 4}$