Question

Determine the domain of (f/g)(x) when f(x)=1/x and g(x)= sqrt x+8
(answer choices in photo)

Answer 1

Answer:

(−8,0)∪(0,∞)

Step-by-step explanation:

This is composition, which I'm going to assume you've covered (sorry if I use any weird terms because of that).

So, anyway, (f/g)(x) is basically $\frac{f(x)}{g(x)}$.

In this case, the answer would be $\frac{\frac{1}{x} }{\sqrt{x+8} }$

I'm going to assume we're using the real number system.

In that case, x can't be less than 0 (can't even be equal to because divide by zero error

So, $\sqrt{x+8} > 0$

Solve for x by squaring.

$\sqrt{x+8} > 0$

$x > -8$

However, in the numerator, there is 1/x. A number divided by 0 is undefined. So, x has to be greater than -8, and it can't be 0.

So, with that, the interval notation is like this.

(−8,0)∪(0,∞)