# functions

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

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ajb    1567

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

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ajb    1567

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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blue89    19

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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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
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studiot    1131

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