Question

The number point f( x)= {x, if x is a rational 0,if x is a irrational } ls continuous at?
a)1 b) infinity (c) 2 (d) 3​

Answer 1

Answer:

At x=0

x→0

+

lim

f(x)=0

(Same for rational and irrational)

Also

x→0

−

lim

f(x)=0

So it is continuous at x=0

At other number it's limit is not defined in it's neighbourhood as it can be x or 0 when x



=0 it is not continuous.

So f(x) is continuous only at 0