Question

Give detailed Conception of : into functions.

Answer 1

@terenzreignz @nader1 @Hope_nicole

Answer 2

@Eyad

Answer 3

I believe @nader1 already defined onto functions last time ^.^

Answer 4

crap, get me on the next one, i dont remember this.

Answer 5

^^ true :P

Answer 6

Help me lol

Answer 7

A function f from A to B is called onto if for all b in B there is an a in A such that f (a) = b. All elements in B are used.

Answer 8

Well, a function from a domain X to a co-domain Y is onto if
for any element y in Y, there exists an x in X such that y = f(x)

In other words, the range of the function is equal to its codomain.

Answer 9

into function...

Answer 10

Are you sure that's not a typo?

Answer 11

into or onto?

Answer 12

Maybe the word "surjective" is there, too.

Answer 13

A function f:A -->B is onto if for every element b in B, there is an element a in A such that f(a) = b. That is, for every element of the codomain, there is an element of the domain that maps to it under f. In other words, the image set (or range) of f is the entire codomain. A function is into simply if every element of A maps to something in B. In other words, if B is a codomain, then f is into. For a function to be into, it is not necessary for every element in B to have an element in A that maps to it, but if it does, f would be onto. So, onto functions are also into, but into functions aren't necessarily onto.

An example of an onto function is f(x) = x, where the codomain is the entire set of real numbers. This is because for every real number x, there is a real number (namely, x again) which maps to x under f. This is also an into function. An example of an into function which isn't onto is f(x) = x^2, where the codomain is all real numbers. Every real number you plug into f will give you an answer in the real numbers (making it into), but there is no real number you can plug into f which will map to a negative real number (so it's not onto).

Answer 14

That's already a bijection, @nader1
Here's another onto function...
f: R -> R
f(x)=tan x

You'll find that for any real number y, there exists a real number x such that
y = tan x

Answer 15

i think that you what i bring from a book lool now i remember

Answer 16

into different from onto ^^

Answer 17

What is into, then?

Answer 18

f:A -> B
By definition, any function would map an element of A to an element of B

So, all functions are into?
I doubt there is even such a concept.

Answer 19

look in the top i explain

Answer 20

@nader1
You said
A function is into simply if every element of A maps to something in B.

Then all functions are into.

Answer 21

Because functions always map an element of its domain to an element of its codomain, that's the definition of a function

Answer 22

Every real number you plug into f will give you an answer in the real numbers (making it into), but there is no real number you can plug into f which will map to a negative real number (so it's not onto).