I am having trouble with this question and I am unsure how to solve it...

True or False (with justification) The function

sin(x) if x ≤ 0
f(x) =
1+cos(x) if x>0

has a jump discontinuity at x = 0.

true, since

sin(0) = 0
1+cos(0) = 2

That is, the left limit is 0
The right limit is 2