is the function x²+3 surjective for real numbers. how do you test for surjectivity in general?

# functions

### #1

Posted 6 June 2016 - 09:17 AM

### #2

Posted 6 June 2016 - 11:09 AM

You should think about solutions to

Can this be solved for any real y? Or can you find at least one y where this equation cannot be solved?

Mathematical Ramblings.

### #3

Posted 6 June 2016 - 11:58 PM

If x is real,

### #4

Posted 7 June 2016 - 05:06 AM

If x is real,

I was hoping markosheehan would reach such a conclusion by himself... I think this question could be homework.

Mathematical Ramblings.

### #5

Posted 27 August 2016 - 11:17 AM

is the function x²+3

for real numbers. how do you test for surjectivity in general?surjective

May I ask what that means ,"surjective" ??

### #6

Posted 27 August 2016 - 01:51 PM

May I ask what that means ,"surjective" ??

A function, f, from set A to set B, is said to be "surjective" (also called "from A **onto** B") if and only if, for every y in B there exist x in A such that f(x)= y.

A function, f, from set A to set B, is said to be "injective" (also called "one to one") if and only if, whenever f(x)= f(y), x= y.

A function, f, from set A to set B, is said to be "bijective" if and only if it is both surjective and injective (for every y in B, there exist one and only one x in A such that f(x)= y). A function is "invertible" if and only if it is bijective.

**Edited by HallsofIvy, 27 August 2016 - 01:52 PM.**

### #7

Posted 27 August 2016 - 04:49 PM

A function, f, from set A to set B, is said to be "surjective" (also called "from A

ontoB") if and only if, for every y in B there exist x in A such that f(x)= y.

A function, f, from set A to set B, is said to be "injective" (also called "one to one") if and only if, whenever f(x)= f(y), x= y.

A function, f, from set A to set B, is said to be "bijective" if and only if it is both surjective and injective (for every y in B, there exist one and only one x in A such that f(x)= y). A function is "invertible" if and only if it is bijective.

Nice and complete +1

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