[Math] The origin of the function $f(x)$ notation

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What are the historical origins of the $f(x)$ notation used for functions? That is when did people start to use this notation instead of just thinking in terms of two different variables one being dependent on the other?

Any references would be appreciated.

Best Answer

The authoritative reference for these matters is the book

Florian Cajori, A History of Mathematical Notations (1929), reprinted by Dover.

On page 268 of volume II, Cajori says that the notation $f(x)$ was first used by Euler in 1734:

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