Function Notation

Sunday 25 September 2005 at 6:17 pm | In Articles | 9 Comments

The notation f(x) is very common and is taught at A level (and sometimes earlier) in the UK. It’s well understood and used but has one well-known flaw – composition of functions. f\circ g or just fg is defined by fg(x)=f(g(x)). The problem here is that fg means do g first then f, rather than the other way round and is therefore counter-intuitive to the beginner.

One solution is to use a different notation for functions and use xf instead of f(x). It’s certainly more economical to write but, more importantly, the composite function fg is defined by x(fg)=(xf)g, which means do f then g. This seems to be much nicer if it weren’t for one thing. As far as I know, this notation is only taught in advanced courses (3rd year degree/postgraduate) and in books like Universal Algebra by P M Cohn, which is certainly not meant to be read by a novice. By this time, the f(x) is so engrained in a student’s mind it is quite difficult to change to xf – it certainly was for me :-?

Does anyone know if the xf notation is taught in more elementary mathematics courses; if so, how was it received?

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