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

1 Answer
Jun 13, 2018

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]}