Question

What is the domain and range of `f(x) = sqrt(x + 5)`?

Answer 1

Domain `[-5,+oo)`, Range: `[0,+oo)`

Explanation:

`f(x) = sqrt(x+5)`

Assuming `f(x) in RR` then `f(x)` is defined `forall x>=-5`

Hence, the domain of `f(x)` is `[-5,oo)`

Now consider, `f(-5) = 0` and `f(x) > 0 forall x > -5`

Also, since `f(x)` has no finite upper bound.

The range of `f(x)` is `[0,+oo)`

We can infer these results from the graph of `f(x)` below.

graph{sqrt(x+5) [-10, 10, -5, 5]}