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#1 markosheehan

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Posted 6 June 2016 - 09:17 AM

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


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#2 ajb

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Posted 6 June 2016 - 11:09 AM

You should think about solutions to

 

 x^2 + 3 - y =0

 

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


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#3 mathematic

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Posted 6 June 2016 - 11:58 PM

If x is real, x^2+3 \ge 3


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#4 ajb

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Posted 7 June 2016 - 05:06 AM

If x is real, x^2+3 \ge 3


I was hoping markosheehan would reach such a conclusion by himself... I think this question could be homework.
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#5 blue89

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Posted 27 August 2016 - 11:17 AM

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

 

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


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#6 HallsofIvy

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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.

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#7 studiot

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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 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. 

 

Nice and complete +1


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