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donmkeys
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i need to prove that the following is not surjective. how do i do that?
let f:R->R be the function defined by f(x)=x^2 + 3x +4.
let f:R->R be the function defined by f(x)=x^2 + 3x +4.
The simplest thing to do is to note that the solutions to the equation [itex]x^2+ 3x+ 4= 0[/itex] are given bydonmkeys said:i need to prove that the following is not surjective. how do i do that?
let f:R->R be the function defined by f(x)=x^2 + 3x +4.
In order for a function to be surjective, every element in the range must have at least one corresponding element in the domain. To prove that a function is not surjective, you can show that there is at least one element in the range that does not have a corresponding element in the domain.
A function is surjective if every element in the range has at least one corresponding element in the domain. In contrast, a function is injective if every element in the range has at most one corresponding element in the domain. In other words, a surjective function "covers" its entire range, while an injective function does not have any repeats in its domain.
To prove that a function is not surjective, you can use a counterexample. This means finding a specific element in the range that does not have a corresponding element in the domain. By showing that even one element does not have a pre-image, you can prove that the function is not surjective.
Yes, a function can be both surjective and injective. This type of function is called a bijection. A bijection is a one-to-one correspondence between the domain and range, meaning that every element in the domain has one and only one corresponding element in the range, and vice versa.
Proving that a function is not surjective is important because it can help you understand the behavior of the function and its relationship between the domain and range. It can also help identify any limitations or restrictions on the function. Additionally, proving that a function is not surjective can be useful in solving various mathematical problems and proofs.