Question

81. For what values of x is f continuous?
f(x) =
0 if x is rational
1 if .r is irrational​

Answer 1

Step-by-step explanation:

For what value of x is f continuous if f(x) = {1 if x is irrational and 0 if x is rational?

Sadly, this function is not continuous at any value b of x, because (speaking informally) in order for f to be continuous at b, then the values of f at values of x that are near b have to be near f(b) - and that doesn’t happen for any value b of x.

If you changed the function so that h(x) = 0 when x is irrational and h(x) = x when x is rational, then h would be continuous at 0, since for values b that are near 0, h(b) would be near h(0). Unfortunately, 0 is the only value of x at which h is continuous.