A function (f:\mathbb{R}\to\mathbb{R}) is to be defined by (f(x)=\sqrt{5-ax^2}). What is the correct condition on (a) for it to be a function on all of (\mathbb{R})?

Correct answer: (\ a\le0) / (a\le0)

The expression (5-ax^2) stays non-negative for all real (x) only when (a\le0). In a square-root function the radicand must be non-negative for every input.