Question

find two functions that are both discontinuous at x=3 but whose sum in continuous at x=3

Answer 1

\[g(x) = abs(x-3), when x \neq 3, and g(x) = 1 when x = 3\]
\[f(x) = 1 for x \neq 3, and f(x) = -1 when x = 3\]

Answer 2

Could you explain this please?

Answer 3

sorry i gave the wrong asnwer. First
g and f are clearly discontinuous at 3
(g+f)(x) = abs(x-3) + 2

lim{x->3} (f+g)(x) = 2


define g(3) = 2 and f(3) = 0 when x = 3
0+2 = 2 which is the same as the limit