I have tried to find the answer to this problem, but have no idea! Please help!!?

Question

find functions f(x) and g(x) such that the lim f(x) as x approaches a does not exist for every a
the lim g(x) as x approaches a does not exist for every a
but the lim f(x) + g(x) does exist for every a

Answer 1

Let f(x) = 1 if x is rational, f(x) = 0 if x is irrational. This function is everywhere discontinuous.

Let g(x) = -f(x). Then f(x) + g(x) = 0, which is continuous everywhere.

Answer 2

sorry i can't help you here...i didn't do too well in math myself....good luck though!