Question

what is the domain of this function 2x+4/x-2

Answer 1

If your function is\[f(x)=\frac{2x+4}{x-2}\]your domain is the set of all x for which your function is 'well defined'. Your function won't be defined for any x such that the numerator becomes zero; that is, for x where\[x-2=0\]which means the function falls apart at\[x=2\]At this point, you'd have\[f(2)=\frac{2(2)+4}{2-2}=\frac{8}{0}\]and you cannot divide by zero (I can explain why if you need it).

There are no other restrictions on x, so your domain is the entire set of real numbers, except x=2.