Difference between $\triangleq$, $:=$, $=$ and $\equiv$ when defining a function

Question

Which of the following notation is a correct definition of the square function?

1. $f(x) \triangleq x^2$
2. $f(x) := x^2$
3. $f(x) = x^2$
4. $f(x) \equiv x^2$

While this question is similar to The meaning of various equality symbols, the aforementioned question and its answers do not address the usage if these symbols in the context of function definition.

Answer 1

Different authors use different conventions. Unless you have a particular reason you need to do something fancier, just write $f(x)=x^2$ -- that's what the vast majority of written mathematics does.