SOLUTION: Find the domain of the function. Domain in the link: http://prntscr.com/fyqy26

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Question 1088423: Find the domain of the function.
Domain in the link: http://prntscr.com/fyqy26
Answer by jim_thompson5910(35256) About Me  (Show Source):
You can put this solution on YOUR website!

Given Function:

Note: If the image doesn't show up, then it's the function g(x) = 1/(x(x+2))

The domain is the set of numbers x where x can be any real number but it cannot be equal to zero, and it also can't be equal to -2
Why can't x equal these values? Because either value makes the denominator x(x+2) equal to zero.

We can see this by solving x(x+2) = 0 for x
x(x+2) = 0
x(x+2) = 0
x=0 or x+2 = 0
x = 0 or x = -2

And we can check each value
Plug in x = 0
x(x+2) = 0
0(0+2) = 0
0(2) = 0
0 = 0

Plug in x = -2
x(x+2) = 0
-2(-2+2) = 0
-2(0) = 0
0 = 0

So that shows how x = 0 or x = -2 makes the denominator x(x+2) equal to zero.

In set builder notation, the domain would be

In interval notation, the domain would be

Effectively we're "gluing" three intervals together. Or put another way, we're poking holes in the number line at -2 and 0 while leaving any other number as part of the domain.