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Let's say you're working with the following problem: Y =√(x-7) You cannot take the square root of a negative number, though you can take the square root of 0. So, set the terms inside the radicand to be greater than or equal to 0. Note that this applies not just to square roots, but to all even-numbered roots. It does not, however, apply to odd-numbered roots, because it is perfectly fine to have negatives under odd roots. Here's how: x-7 ≧ 0 Now, to isolate x on the left side of the equation, just add 7 to both sides, so you're left with the following: x ≧ 7 Here is how you would write it: D = [7,∞) Let's say you're working with the following function: Y = 1/√( ̅x2 -4). When you factor the denominator and set it equal to zero, you'll get x ≠ (2, - 2). Here's where you go from there:  Now, check the area below -2 (by plugging in -3, for example), to see if the numbers below -2 can be plugged into the denominator to yield a number higher than 0. They do. (-3)2 - 4 = 5  Now, check the area between -2 and 2. Pick 0, for example. 02 - 4 = -4, so you know the numbers between -2 and 2 don't work.  Now try a number above 2, such as +3. 32 - 4 = 5, so the numbers over 2 do work.  Write the domain when you're done. Here is how you would write the domain: D = (-∞, -2) U (2, ∞)
Write the problem. Set the terms inside the radicand to be greater than or equal to 0. Isolate the variable. State the domain correctly. Find the domain of a function with a square root when there are multiple solutions.