Question

Let a function :f R → R be defined by


f(x)={2 if x∉Q

4 if x∈Q}


Check whether f is continuous on B.

Answer 1

Let us analyze the given in [1,2]

so between 1 and 2 there are many irrational number numbers like $\sqrt2 \ and\ \sqrt3$ and as we know that after every irrational number there is a rational number so the graph of the function will be stripped one

Hence the function is discontinuous