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# What does f:x-> mean? Mathematics notation watch

1. I'm currently doing some C3 and have noticed the notation f: x -> appear a few times, please can someone help with with what this means?

also could I for instance substitute in Y for f:x ->
2. (Original post by NoahMal)
I'm currently doing some C3 and have noticed the notation f: x -> appear a few times, please can someone help with with what this means?

also could I for instance substitute in Y for f:x ->
The function f is such that each value of x maps onto...
It is basically the same as f(x) for c3.

so f: x -> x^2 means f(x) =x^2
3. Just means f is a function of x
4. It's the right notation for a function.

Functions are defined from a domain to a codomain (C3 probably calls it the range, if I remember). This notation is quite explicit about it from this point of view: f : [thing in domain] -> [thing in codomain]. Technically, it should specify what the domain and range are, but during A levels, these are exclusively and (i.e., real numbers, and positive real numbers).

Why do I say this is the right notation? Because whenever you write things like f(x), you should be aware that the function is f, not
f(x). f(x) is the result of having applied f to x. It is a member of the codomain!! To be more precise about the connection between these two notations, you can write (unhelpfully). That obviously tells you nothing about the function, but it shows you what the point is.

As a concrete example, you should simply think of as a function on real numbers as a shorthand for

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