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What are even and odd periodic extension of a function?
Even and odd periodic extensions of a function are methods to extend a given function to a periodic one. An even periodic extension creates a function that is symmetric around a vertical axis, meaning it satisfies ( f(x) = f(-x) ) for all ( x ). In contrast, an odd periodic extension results in a function that is antisymmetric, satisfying ( f(x) = -f(-x) ). These extensions are useful in signal processing and Fourier analysis, as they help simplify calculations and analyze the behavior of functions over specified intervals.
Function notation fx is read as?
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.
What is a domain for f(x) 2x2-3?
The function ( f(x) = 2x^2 - 3 ) is a quadratic function, which is defined for all real numbers. Therefore, the domain of ( f(x) ) is ( (-\infty, \infty) ). This means you can input any real value for ( x ) into the function.
What does odd function mean?
An odd function is a type of mathematical function that satisfies the condition ( f(-x) = -f(x) ) for all ( x ) in its domain. This means that the graph of the function is symmetric with respect to the origin; if you rotate the graph 180 degrees around the origin, it remains unchanged. Examples of odd functions include ( f(x) = x^3 ) and ( f(x) = \sin(x) ).
What does f of x cubed mean?
In mathematics, ( f(x^3) ) refers to the function ( f ) evaluated at the cube of ( x ). This means you first take the input ( x ), cube it (i.e., raise it to the power of 3), and then substitute that value into the function ( f ). For example, if ( f(x) = x + 1 ), then ( f(x^3) = x^3 + 1 ).
What is a periodic function?
f is a periodic function if there is a T that: f(x+T)=f(x)
What are even and odd periodic extension of a function?
Even and odd periodic extensions of a function are methods to extend a given function to a periodic one. An even periodic extension creates a function that is symmetric around a vertical axis, meaning it satisfies ( f(x) = f(-x) ) for all ( x ). In contrast, an odd periodic extension results in a function that is antisymmetric, satisfying ( f(x) = -f(-x) ). These extensions are useful in signal processing and Fourier analysis, as they help simplify calculations and analyze the behavior of functions over specified intervals.
What are periodic functions?
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.
What is fourier series?
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.
Explain why f represents the graph of a function?
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'
What does function notation means?
Function notation means the function whose input is x. The mathematical way to write a function notation is f(x).
What is fxfxf is it f cubed?
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.
What is the composition of an even and an odd function?
For an even function, f(-x) = f(x) for all x. For an odd function, f(-x) = -f(x) for all x.
Which functions has a period?
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).
What is the solution for function of function of x equals function of x?
f(f(x)) = f(x). Only if f is 1-1 then we have a solution f(x)=x.
Function notation fx is read as?
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.
In mathematics what does compose mean?
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.
