These two problems appear in my textbook:
Give a function f: R to R continuous only at x = 0 and x = 1.
For this, let f(x) = x^2 if x is rational and x if x is irrational.
Then it is continuous only at x^2 = x which implies x equals 0,1.
Give a function f: R to R continous only at x1, x2,....,xn.
This one I'm not really sure what to do. Can you do something similar to the first one?
Any help would be appreciated.