Question

Give an example of a radical function f(x) whose domain is (3,∞) and whose range is (-∞, 0].

Answer 1

Examine these four functions:
\(\rm f=-\sqrt{x-3}\)
\(\rm g=-\sqrt{x}-3\)
\(\rm h=-\sqrt{x+3}\)
\(\rm \ell=-\sqrt{x}-3\)

One of these gives us the desired domain and range.
I'll leave you to think about it a bit :)

Answer 2

presume it means the domain is \[[3,\infty)\] right?

Answer 3

Ooo I hope so :O