- #36
CaptainAmerica17
- 59
- 10
LolWWGD said:
LolWWGD said:Us non-superheroes tend to do that ;). Thanks for the setup.
An injective function is a function in which each element in the domain maps to a unique element in the range. This means that for every input, there is only one possible output.
To prove that a function is injective, you must show that for any two distinct inputs in the domain, the corresponding outputs in the range are also distinct. This can be done through various methods such as algebraic manipulation, using the definition of injectivity, or using a proof by contradiction.
The notation f(x) represents a function, where x is the input or independent variable and f(x) is the output or dependent variable. It is read as "f of x" or "f at x". The function f maps the input x to the output f(x).
Yes, a function can be both injective and surjective. A function that is both injective and surjective is called a bijective function. This means that every element in the domain has a unique corresponding element in the range, and every element in the range has at least one corresponding element in the domain.
Injectivity is represented mathematically using the notation f(x) = f(y) implies x = y. This means that if two inputs in the domain have the same output in the range, then the inputs must be equal. In other words, each output in the range is associated with only one input in the domain.