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

1 Answer
Jun 13, 2018

Answer:

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]}