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

1 Answer
Apr 23, 2017

Answer:

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))#