No.
In mathematics, the modulus of a real number is its numerical value without regard to its sign. So, for example, 3 is the absolute value of both 3 and −3. When graphing a modulus function, f(|x|), graph the function f(x) ignoring the modulus and simply reflect any values below the x-axis (negative values) so they become positive.
At the basic level, the modulus of a number or expression is simply the value of the number or of the expression. For a positive number the modulus is the number, for 0 it is 0, and for a negative number, x, it is -x (which is positive).
In mathematics, an "onto" function, or surjective function, is one where every element in the target set has at least one corresponding element in the domain. In contrast, an "into" function is not necessarily onto; it maps some elements from the domain to the target set, but not every element in the target set must be hit by the mapping. Therefore, while all onto functions can be considered into functions, not all into functions are onto.
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.
No.
Calculating the modulus of two numbers. Are you surprised now?
No. The modulus function maps two values (except 0) from the domain (-x, and x) to one value (+x) in the range or codomain. This means that for the inverse mapping each value in the new domain (the original codomain) is associated with two values in the new codomain (original domain). A function cannot map one value to more than one.
In mathematics, the modulus of a real number is its numerical value without regard to its sign. So, for example, 3 is the absolute value of both 3 and −3. When graphing a modulus function, f(|x|), graph the function f(x) ignoring the modulus and simply reflect any values below the x-axis (negative values) so they become positive.
Taking the modulus of the wave function allows us to obtain the probability density of finding a particle at a particular position in quantum mechanics. This is because the square of the modulus of the wave function gives us the probability of finding the particle in a given volume element.
At the basic level, the modulus of a number or expression is simply the value of the number or of the expression. For a positive number the modulus is the number, for 0 it is 0, and for a negative number, x, it is -x (which is positive).
Inverse of a function exists only if it is a Bijection. Bijection=Injection(one to one)+surjection (onto) function.
The MOD function finds a modulus. That is the remainder when you divide one number into another. So if you divide 10 by 3, you would get a remainder of 1. To do that with the MOD function, you enter it as: =MOD(10,3)
It is a bijection [one-to-one and onto].
It is; everywhere except at x = 0
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.
Assuming the domain and range are both the real numbers (or rationals): Yes, it is 1 to 1 Yes, it is onto and the inverse is x = (y-3)/4