What are the discontinuities of the function f (x) = x<2-36/4x-24?

Well, 2-36/4x-24 is the same as (2-24) - (36/4) x which simplifies to - 22-9x. This does not have a discontinuity anywhere. If you meant to divide 36 by 4x, then x=0 would be the discontinuity since you cannot divide by 0. If you meant to have 4x-24 all in the denominator, then x=6 is the discontinuity since that would make the bottom equal 0. So it seems you need some parenthesis here somewhere for your problem to make sense.