# Find the domain of the function

x≤0.5 or x>12 is the answer but I don't understand how. The denominator should not be equal to zero and a square root cannot take negative numbers. So how is the answer x≤0.5 ? Shouldn't it be x>=0.5 and x is not equal to 12?

Thanks for the help:)

If $$x\lt0.5$$, then both numerator and denominator of $$(8x-4)/(x-12)$$ are negative, so the quotient is positive, hence the square root can be taken. If $$0.5\lt x\lt12$$, then the numerator is positive but the denominator is negative.