Respuesta :

Let's consider what we are asked. The domain is defined as a set of points that satisfy the equation on the x-ordinate.
So, essentially, we need to find if and what the restriction on x is.

Let's now consider just f(x) because g(x) is completely irrelevant to the question.

f(x) = 2 - x^(1/2)
Since f(x) can never be 0 for a defined function, let's consider when f(x) = 0 to find a restriction on x.

2 - x^(1/2) = 0
2 = x^(1/2)
+-4 = x

But we can only take the positive 4 because inside a square root has to always be positive (unless you're dealing with complex numbers), so the only restriction is that x cannot be equal to 4.

Therefore, our domain is: x >= 0; x =/= 4
facundo3141592

We will see that the domain of the rational function is:

D : {x| x ≥ 0, x ≠ 4}

How to get the domain of a function?

We start by assuming that the domain of a function is the set of all real numbers, and then we remove the problematic points, where a problematic point would be a value of x that makes a denominator equal to zero, or something like that.

Here we have two functions and a rational function, that is given by the quotient of the first two:

[tex]f(x) = 2 - \sqrt{x} \\\\g(x) = x^2 - 9\\\\g(x)/f(x) = \frac{x^2 - 9}{ 2 - \sqrt{x}}[/tex]

So, we start by assuming that the domain is the set of all real numbers, and then we remove those that make the denominator equal to zero, so we need to solve:

2 - √x = 0

2 = √x

There is only one solution for this, which is:

x = 4

Another thing we can notice here is that we can't input negative values in a square root, then we need to remove all of these from the domain.

Concluding, the domain is:

D : {x| x ≥ 0, x ≠ 4}

If you want to learn more about domains, you can read:

https://brainly.com/question/1770447

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