What is the domain of the function?

The domain is always real numbers, unless x is in the denominator or under a square root. If that happens, whatever values make the denominator 0 are excluded from the domain. Or whatever values make the square root negative are excluded from the range.

4x + 12 = 0

4x = -12
x = -3

The domain is all real numbers except at x = -3.

x > -3 or x < -3

The domain written in interval notation is:

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