Math GRE Practice Test Question
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}.
Then the set of numbers at which g is continuous is
A empty set
B {0}
C {1}
D the set of rational numbers
E the set of irrational numbers
The answer is B, and I don't understand why. I chose D. If we're going to choose set with a single element, why isn't {1} just as correct as {0}?
g(x) = {1 if x is rational and ex if x is irrational}.
Then the set of numbers at which g is continuous is
A empty set
B {0}
C {1}
D the set of rational numbers
E the set of irrational numbers
The answer is B, and I don't understand why. I chose D. If we're going to choose set with a single element, why isn't {1} just as correct as {0}?