how do i prove that a function is a legitimate function ?

Question

how do i prove that a  function is a legitimate function ?

anonymous · Answer

None of the elements in the domain are repeated.

Depends on what you have.

jenniferjuice · Answer

i have f(x) = 2x + 5

anonymous · Answer

Do they want a formal proof, or just yes or no?

jenniferjuice · Answer

it says i have to use complete sentences to prove its a legitimate function

anonymous · Answer

You could say multiplication and addition are closed on real numbers, so it is defined for all real numbers.  Then you can say there is no way that any two outputs would have the same input, since multiplication and addition will lead to a single output.

jenniferjuice · Answer

so if i said 
F(x) =2x + 5 is a legitimate function because  its defined for all real numbers since addition  and multiplication are closed on real numbers. It is not possible for any two outputs to have the same input because multiplication and addition will lead to a single output.

anonymous · Answer

Basically, but you need to understand what it means