Question

Determine the domain of the function
f(x)=(2-x)/√(12-x^2 )

Answer 1

\[-2\sqrt{3}<x<2\sqrt{3}\]

Answer 2

Do you know why? @theworldfines1

Answer 3

I see this got bumped. Still have a question about it?

Answer 4

sqrt(12-x^2)=0
x=sqrt(12)
x=+2(sqrt(3))
x=-2(sqrt(3))
it should not be between these

Answer 5

To be honest guys, I'm still not seeing it. What happens to (2-x) in this. Did I miss something?

Answer 6

I am doing domains and ranges in my college calculus class right now. I have no clue how it works. If you figure it out... mind giving me some advice??

Answer 7

To find the domain of this function:

You can not take the square root of a negative number, so the part inside the square root must be greater than or equal to zero. BUT you also can not divide by zero, so the part inside the square root must be greater than zero \[\Large 12-x^2 > 0\] which you need to solve

Answer 8

f(x)=(2-x)/√(12-x^2 )

remember that you can't divide by zero, so √(12-x^2 ) can not be equal to zero. And since you can't square root a negative, then (12-x^2) > 0.

Answer 9

@theworldfines1 Because it is a question of domain and (2-x) would be valid no matter what, NOTHING happens to (2-x). That is why everyone is looking at the bottom of the fraction and inside the root. It if was range, there might be a difference... I didn't do the numbers to see.

\(f(x)=\dfrac{2-x}{\sqrt{12-x^2}}\)

Now a good graph can help show both. Do not trust graphs, because they do not always give good values, but they are great indicators. For example, look at the graph of this:
https://www.desmos.com/calculator/e01sq9occy

From that, you might think the domain of x was \(-3.5<x<3.5\) when it is really a small bit closer to 0 than that. That is why the math is more accurate than the graph, but the graph is still useful. It lets you do a sanity check on your answers. Do the math first and then graph. If they do not match, find out why!