Consider the following property that a function f :R → R may or may not have: For all functions g: R → R, if lim g(x) does not exist, then lim ( f (x) + g(x) ) does not exist. Prove that f(x) has this property if and only if lim f(x) exists. (You can use the standard properties of limits that you know from calculus; the relevant ones are all proven in the course notes. Make sure that you use such properties correctly (in particular, make sure that the hypotheses are satisfied) You do not need to use the definition of limit for this problem. You might consider alternative ways to formulate some of the statements involved)