What is the domain of g(x) = sqrt(-3x - 2)?

1 Answer
Feb 4, 2016

Given function is g(x)=\sqrt{-3x-2}

Now, one thing for sure is that we can't have a real valued function involving imaginary outputs. So that means the values under the square root should be positive.

So, from the function itself \sqrt{-3x-2}=0 is the least possible value. Squaring and rearranging on both sides we get
-3x=2\impliesx=(-2)/3

But what side of the real numbered line should be included? Left side of -2/3 or the right?
So again, we take the square root, and then square and rearrange, but this time, we say that the function inside the square root should be positive.

In a more simple way of saying it mathematically
-3x-2>0\implies-3x>2\impliesx<-2/3 (I've multiplied the inequality by a negative value, that's why the sign reverses).

So in the end, x belongs to the real number set, containing the values (oo,(-2)/3]