Teaching in the UK, I have noticed that all the exam boards (OCR, Edexcel, AQA, MEI) the following notation for functions and composite function.
- Functions are written in roman upshape (e.g. $\mathrm{f} : A \to B$, $y = \mathrm{g}(x)$, etc.) rather than in italic.
- If $\mathrm{f}$ and $\mathrm{g}$ are functions, the composite function is written as $\mathrm{gf}(x) = \mathrm{g}(\mathrm{f}(x))$.
Apart from the exam boards, and the textbooks endorsed by the exam boards, however, this is actually the first time I see this notation, for all my undergraduate and graduate book use the notation $g\circ f$ to denote the composite function, defined as $(g \circ f)(x) = g(f(x))$. I have tried to look up for any reference of usage of this confusing notation, which many of my students keep confusing with the product of two functions, but I have not been able to find any undergraduate/graduate textbook using this notation. So, my questions are:
- Do you know any textbook using this notation, and if so, can you please give me the reference?
- Is there a particular reason why someone should use the notation $\mathrm{g}\mathrm{f}$ instead of $g \circ f$ to denote the composite function?
Generally mathematicians coming from different experiences have different taste for notation, but this is not like the upshape vs italic 'd' in an integral or in the derivative, that is evenly distributed between those who use one and those who use another: I actually have not been able to find a single reference, beside Wikipedia, mentioning the notation (as $gf$ rather than $\mathrm{gf}$), but quoting a book that actually uses the notation $g\circ f$.
Thank you to whoever has any information that might help me understand the choice of the exam boards. (Bu the way, I have tried to question the exam board, but my query has remained unanswered.)