We'll say a function funhelpfulataif, whenever g is a function such that lim x goes to a of g (x) does not exist, then lim x goes toaof (f(x)+g(x)) also does not exist. Prove that a function f is unhelpful at a if an only if lim x goes to a of f(x) does exist.

I'm having trouble reading this problem. Can anyone phrase it in another way that might make more sense?

Right now I understand the for f(X) to be considered an unhelpful function

(1) the limit of f(x) as x goes to a must exist.

(2) the limit of g(x) as x goes to a does not exist

(3) the limit of (f(x)+g(x)) as x goes to a does not exist

In condition 3, if we know that the limit of the sum is equal to the sum of the limits, then we know that the limit of f(x) as x goes to a and the limit of g(x) as x goes to a must both not exist. How can that be if we also know in condition 1 that the limit of f(x) as x goes to a must exist?