In order to find the domain of √x+4, we need to understand what domain is. A domain is, in essence, any real number x that produces a real number y.
So, looking at √x+4, we must ask at what value x does the function (equation) stop producing a number that is real? In other words, not an irrational number.
We know that the square root of a negative number produces a non-real number, thus using the definition of domain we will simply find when does x stop giving us real y values.
The first step to solving this now is to look at the x+4 itself and disregard the square root. Let's set x+4 to equal zero so: x+4=0. Then subtracting 4 from both sides, we discover that x=−4.
Plug x=−4 into √x+4, so √−4+4. This will be √0 which is basically 0. At x=−4, the function still gives us a real number. What if we plug in x=−5? We get √−1 which will result in an irrational number.
Discovering this, we can now conclude that the domain of x starts at x=−4. Thus we will get x≥−4.
Now, let's look at √x+4 and ask does it ever hit zero if we go towards the positive x-axis? No, it doesn't. Due to this, x≥−4 will be our final answer. It can also be written as [−4,∞).