That is a function defined as: f(x) = -1 if x is negative f(x) = 0 if x is zero f(x) = 1 if x is positive In other words, a function that basically distinguishes whether the input is positive, negative, or zero.
If y is an exponential function of x then x is a logarithmic function of y - so to change from an exponential function to a logarithmic function, change the subject of the function from one variable to the other.
Yes, the word 'function' is a noun (function, functions) as well as a verb (function, functions, functioning, functioned). Examples: Noun: The function of the receptionist is to greet visitors and answer incoming calls. Verb: You function as the intermediary between the public and the staff.
yes
That's true. If a function is continuous, it's (Riemman) integrable, but the converse is not true.
both
The signum function is differentiable with derivative 0 everywhere except at 0, where it is not differentiable in the ordinary sense. However, but under the generalised notion of differentiation in distribution theory, the derivative of the signum function is two times the Dirac delta function or twice the unit impulse function.
2/s
The Fourier transfer of the signum function, sgn(t) is 2/(iω), where ω is the angular frequency (2πf), and i is the imaginary number.
bijective
It is a bijective function.
Domain, codomain, range, surjective, bijective, invertible, monotonic, continuous, differentiable.
The function is called the signum function, or sign(x). It is equal to abs(x)/x
The sign function is used to represent the absolute value of a number when used in trigonometry. It is also referred to as the signum function in math.
I have no idea about the signam function.The signum function is odd because sgn(-x) = -sgn(x).
No. The function y = x2, where the domain is the real numbers and the codomain is the non-negative reals is onto, but it is not one to one. With the exception of x = 0, it is 2-to-1. Fact, they are completely independent of one another. A function from set X to set Y is onto (or surjective) if everything in Y can be obtained by applying the function by an element of X A function from set X to set Y is one-one (or injective) if no two elements of X are taken to the same element of Y when applied by the function. Notes: 1. A function that is both onto and one-one (injective and surjective) is called bijective. 2. An injective function can be made bijective by changing the set Y to be the image of X under the function. Using this process, any function can be made to be surjective. 3. If the inverse of a surjective function is also a function, then it is bijective.
Here are some examples:Domain, codomain, range, surjective, bijective, invertible, monotonic, continuous, differentiable.