Math GRE Practice Test Question

[iconoclass]

Question: Let g be the function defined on the set of all real numbers by
g(x) = {1 if x is rational and ex if x is irrational

Comments

[just_you_wait]

As x approaches 0, g(x) approaches 1, in both the rational and irrational cases (note that e^0 is 1). This can't be said for any other value.

Recall the conditions necessary for continuity at a point - the function is defined, has a limit, and the value equals the limit. Nowhere besides at 0 does a limit exist.