Denoting a Restricted Function

[Hootenanny]

How does one denote a restricted function?

For example, suppose I have a function $F : \mathbb{R}\to\mathbb{R}$, how would I denote a new function f, such that f is the restriction of F to the positive semi-axis? Up until this point I would have just said that f is the restriction of F to the positive semi-axis, but it occurs to me that there should be a more concise way of writing it.

 

[MathematicalPhysicist]

f(x)=F(x) for only x positive real number, there's not a lot about it.

 

[Tac-Tics]

$$f\vert_S$$ is the standard notation for the restriction of f to a subset S of f's domain.

 

[Hootenanny]

$$f\vert_S$$ is the standard notation for the restriction of f to a subset S of f's domain.

That's exactly was I was looking for Tac-Tics.

Thanks to you both.