the function f(x)= { 0 , if x is irrational
{ 1 , if x is rational is :
a) continuous at x=1
b) discontinous only at 0
c)discontinous only at 0, 1
d) discontinous everywhere
The function f defined by f(irrational) = 0
and f(rational) = 1
is bounded but not integrable since its set of discontinuity points is not a zero set (since it is discontinuous everywhere).
and f(rational) = 1
is bounded but not integrable since its set of discontinuity points is not a zero set (since it is discontinuous everywhere).