Function - injection

[radagost]

Hi everyone . I need a little help. The exercise goes as follows: If f: A[tex]\rightarrow[/tex] [tex](-\infty,0][/tex], and the function: [tex]f(x)=-(x-3)^2[/tex]. Determine A such that the given function is injective. When I've tried to get the right answer I got two valid solutions : [tex](-\infty,3] or[/tex][tex][3,+\infty)[/tex]. I might be wrong but anyone's answer or suggestion will be more than helpful .

[Guest]

Actually, there are infinitely many "valid solutions", [tex](-\infty, 3][/tex] and [tex][3, \infty)[/tex] are the two "maximal solutions" and any subset of either of those is also a "valid solution".

[radagost]

According to two maximal solutions, may i pick any of them or should I include both as possible solutions? Anyway, thank you for answer!

[Guest]

From my reading of the problem either [tex](-\infty, -3][/tex] or [tex][3, \infty)[/tex] is a good answer but to be safe (or perhaps just to show off!) I would give both.