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

1 Answer
Jul 7, 2017

x4 or [4,)

Explanation:

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 x4.

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, x4 will be our final answer. It can also be written as [4,).