What does "$\,g=f|Y\,$" mean, where $g$ and $f$ are functions and $Y$ is a subset of the domain of $f$?

Question

What does "$\,g=f|Y\,$" mean, where $g$ and $f$ are functions and $Y$ is a subset of the domain of $f$?

Answer 1

$f|Y$ means the restriction of $f$ to $Y$. For example, the restriction of $y=x^2$ to $x\geq 0$ gives you the "right half" of the parabola.