I am having a little problem with proving that these functions are continuous.

1) f(x) = (x+1+|x-2|)/(|4-x|+2x);

It is clear that the function is defined for all x belonging to R - {-4}. But how do I prove that the function is continuous on this interval.

2) f(x) defined on the interval [0,1] by:

f(x) = x (if x belongs to Q)

f(x) = 1 - x (if x does not belong to Q)

Show then that f(x) is continuous in only one point, and that point is 1/2.

Thanks in advance for the help guys.