f(x) is just a way of saying a function of x, instead of saying "y=3x" you can write
f(x) (3x), or in the case of a periodic function, you might have something like f(x) = sin(x).
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If it were written in a book of some sort, fx or f(x) is read aloud as "f or x". "f" is a function of some variable, "x". By function it means something happens to x e.g. x2 or 3x+4.
It means that the value of the function, f(x), is negative when x = 0.
A function f(x) of the variable x, has a period k where k is some constant, if f(x+ k) = f(x) for every x. It is easy to show that f(x + nk) = f(x) for any integer n. What the above two formulae imply is that the values of the function repeat after an interval (or period) of k. The trigonometric functions are some of the better known periodic functions.
It means the value of the function equals zero when the argument is 4. For example: f(x)=x-4 f(4)=4-4=0
'Y' is a function 'f' of 'x': Y = f(x) . 'Z' is a function 'g' of 'y': Z = g [ f(x) ] .