How do you find the domain and range of f(x) = sqrt(x+6) /( 6+x)?

1 Answer
MeneerNask
Apr 23, 2017

Domain : x!=-6 from the denominator.
x>=-6 as an argument for a square root.

Explanation:

Together we get domain x> -6

Range:
Both the numerator and the denominator are now always positive.

So the range is 0 < f(x) < +oo
graph{1/(sqrt(x+6)) [-10, 10, -5, 5]}
Note:
You may have noticed that 6+x=x+6=(sqrt(x+6))^2, so under the given conditions we may rewrite:
f(x)=cancel(sqrt(x+6))/(sqrt(x+6))^cancel2=1/(sqrt(x+6))

Related questions
See all questions in Domain and Range of a Function
Impact of this question
3364 views around the world
You can reuse this answer
Creative Commons License