Can u gave me some examples of injective function.

In summary, an injective function is one where each input has a unique output, but not all outputs are covered by the function. For example, the function f(n)=3n defined on the set of natural numbers is injective, but not surjective, as there are some outputs (such as 1) that are not covered by the function. Other examples of injective functions can be found, such as the identity function on the interval [0,1] and the identity function on the set of real numbers mapped to the set of complex numbers.
  • #1
yaho8888
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can u gave me some examples of injective function that is not surjective.
Is f(x)=y a injective function that is not surjective?
 
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  • #2
what about f:N--->N defined by f(n)=3n where n is from naturals, and N is the set of naturals.

1-->3
2-->6, so this function is injective since when f(n_1)=f(n_2)=>3n_1=3n_2=>n_1=n_2, but it is not surjective since there exists at least a numberf in the second N, in our case for example 1 that there are no numbers in N(the domain) such that when f(n)=1.
 
  • #3
You can go and define such functions as much as you wish, for i just made that example up. OR are you looking for any other example in particular?
 
  • #4
f:[0,1] -> R given by the identity function.

f:R -> C given by identity function.
 

FAQ: Can u gave me some examples of injective function.

1. What is an injective function?

An injective function is a type of function in mathematics where each element in the domain has a unique corresponding element in the range. This means that no two elements in the domain will map to the same element in the range.

2. What are some examples of injective functions?

Some examples of injective functions include:

  • f(x) = x, where x is any real number
  • f(x) = x2, where x is any positive real number
  • f(x) = ex, where x is any real number

3. How can you determine if a function is injective?

To determine if a function is injective, you can use the horizontal line test. This means that if you draw a horizontal line on a graph of the function, it should only intersect the function once. Additionally, you can also check if the function has a unique output for each input.

4. Are all one-to-one functions also injective?

Yes, all one-to-one functions are also injective. This is because a one-to-one function, by definition, will have a unique output for each input, which is the same requirement for an injective function.

5. What makes an injective function different from a surjective function?

An injective function differs from a surjective function in that an injective function requires each element in the domain to have a unique corresponding element in the range, while a surjective function requires each element in the range to have at least one corresponding element in the domain.

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