The function symbol f(x) was first used by Leonhard Euler (1707-1783)
in 1734 in Commentarii Academiae Scientiarum Petropolitanae (Cajori,
vol. 2, page 268).
Absolute value function. Karl Weierstrass (1815-1897) used | | in an
1841 essay "Zur Theorie der Potenzreihen," in which the symbol appears
on page 67. He also used the symbol in 1859 in "Neuer Beweis des
Fundamentalsatzes der Algebra," in which the symbol appears on page 252.
This latter essay was submitted to the Berlin Academy of Sciences on
December 12, 1859. These are the two reference shown by Cajori (vol. 2,
page 123).