Question

Give an example of a radical function f(x) whose domain is (3,∞) and whose range is (-∞,0]
Can i plz get help

Answer 1

sqrt (x-3) is real only to the right of x=3

so try
-1/sqrt(x-3)

Answer 2

Well, we know that √x has a domain of x>=0, so we could try

√(x-3)

but that has domain [3,∞) and we want to exclude 3. So, let's divide, since we cannot divide by zero:

y = -1/√(x-3)

Now 3 is excluded, and luckily, the range is now also correct. You can check at wolframalpha.com to see:

http://www.wolframalpha.com/input/?i=-1%2F%E2%88%9A%28x-3%29

scroll down a bit past the graph, and it lists the domain and range.