How do you find the domain of f(x)=sqrt(x+4)?

1 Answer
Jul 7, 2017

x>=-4 or [-4, oo)

Explanation:

In order to find the domain of sqrt(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 sqrt(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 sqrt(x+4, so sqrt(-4+4). This will be sqrt(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 sqrt(-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 sqrt(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, oo).