The given function is F(x) = (2-x)/(12x^2+8x)
The domain of a function is the set of all possible values of x for which the function is defined. In this case, the function is defined for all values of x except those that make the denominator equal to zero, since division by zero is undefined.
So, to find the domain of the function, we need to find the values of x that make the denominator equal to zero and exclude them from the domain.
12x^2+8x = 0
4x(3x + 2) = 0
x = 0 or x = -2/3
Therefore, the domain of the function F(x) is all real numbers except 0 and -2/3. In interval notation, we can write the domain as:
(-∞, -2/3) U (-2/3, 0) U (0, ∞)