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.
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 that the value of the function, f(x), is negative when x = 0.
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) ] .
f is a periodic function if there is a T that: f(x+T)=f(x)
A nonconstant function is called periodic if there exists a number that you can add to (or subtract from) the argument and get the same result. The smallest such positive number is called the period. That is, nonconstant function f(x) is periodic, if and only if f(x) = f(x + h) for some real h. The smallest positive such h is the period. For example, the sine function has period 2*pi, and the function g(x) := [x] - x has period 1.
Consider a periodic function, generally defined by f(x+t) = f(x) for some t. Any periodic function can be written as an infinite sum of sines and cosines. This is called a Fourier series.
if the question is why is it labelled as f(x) ? it means the function (the 'f') at a certain x value. saying f(x) is said as 'f at x'. it's the same as saying 'function at x'
Function notation means the function whose input is x. The mathematical way to write a function notation is f(x).
The expression fxfxf means f(f(x)f(x)), where f(x) is a function of x. This is not equivalent to f cubed (f^3(x)), which would mean f(f(f(x))). In fxfxf, the function f(x) is applied twice to the input x, whereas in f cubed, the function is applied three times. The two expressions are different due to the number of times the function is applied to the input.
For an even function, f(-x) = f(x) for all x. For an odd function, f(-x) = -f(x) for all x.
f(f(x)) = f(x). Only if f is 1-1 then we have a solution f(x)=x.
You can invent any function, to make it periodic. Commonly used functions that are periodic include all the trigonometric functions such as sin and cos (period 2 x pi), tan (period pi). Also, when you work with complex numbers, the exponential function (period 2 x pi x i).
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.
A function f(x) is Even, if f(x) = f(-x) Odd, if f(x) = -f(-x)
That is related to "composition", the composition of functions. That means you apply one function after another. f(g(x)) means you first apply function "g" to the variable "x", then you apply function "f" to the result.