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- Dec 4th 2007, 01:39 PM #1

- Joined
- Sep 2007
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- Dec 4th 2007, 01:46 PM #2

- Dec 4th 2007, 02:15 PM #3
Well, you can't take the square root of a negative number , so everything inside the square root, must be positive. (if you have difficulty seeing this, ask yourself what real number multiplied by itself will return a negative number? for example what number squared would be negative 1? There is not one, because a negative number squared will become positive, and a positive number squared will remain positive)

So

Now, if h(x) is positive, but was negative (or vice versa), it must have been equal to zero at some point, because zero is where signs change. So lets find where this equation equals zero.

Factor into (x-1) and (x+1)

so

and

Now, we know where the function equals zero, which is where it changes signs. We just need to check the intervals.

The intervals are

So lets pick the point -2 to check the sign of the first interval, 0 to check the sign of the second interval, and 6 to check the sign of the third interval.

let

is in the domain

is not in the domain

is in the domain

(note, we used brackets on -1 and on 5, because they are roots, which means they cause the equation to equal zero, and we can take the square root of zero, so they are in the domain)

So the domain is:

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Now you try for