find domain in interval notation fx log86x x sqrtx51Solut

find domain in interval notation

f(x) = log₈(-6x) - |x| / (sqrt(x+5)-1)

Solution

I understand this is the function :f(x) = log8(-6x) - |x|/[sqrt(x+5) -1]

we have to see where f(x) exists in real plane.

Now -6x>0 ---> x<0

Further denominator should not be zero : x +5>=0

x>=-5

So, combining the two above Domain: [-5 , 0)