If f(x)= 2 - x^1/2 and g(x)= x^2 - 9 , what is the domian of g(x) divided by f(x) ?

Question

I think it might be B but I am unsure please help if you can!!

Answer 1

First, let's write down the resulting function if we divide g(x) by f(x),

g(x) = x² - 9

f(x) = 2 - x^1/2

g(x) / f(x) = (x² - 9) / (2 - x^1/2)

To determine the domain of this function, we need to ask, "What values of x will result in the function being undefined?" These are the values that we will exclude from our domain.

For this example, the only time the function will be undefined, is when the denominator is equal to 0. So, we can set the denominator equal to 0 to find the value of x which we must exclude from our domain.

2 - x^1/2 = 0

2 = x^1/2 [adding x² to both sides]

4 = x [squaring both sides]

Therefore, if x = 4, then the function is undefined.

We can write the domain of this function in interval notation as follows,

(-∞,4)U(4,∞)

Answer 2

Hello Maya C.,

My name is Jeff S... glad to share some math with you!

So the division of functions is (x² - 9) / 2 - (radical) x... correct?

For this domain problem, there are two things to consider: the number under the radical must be 0 or positive, and the denominator cannot be 0.

So for radical x, the values of x must be 0 or positive: x ≥ 0, so that there are no negative numbers under the radical.

Also, 2 - radical x ≠ 0, or the quotient would be undefined. Solving, radical x = 2 and so x = 4.

So the domain is x ≥ 0, and x ≠ 4.

In interval notation, this is [0, 4) ∪ (4, ∞).