Let f: R → R be defined by f(x) = {(x, x is irrational),(1 - x, x is rational) then f is … (a) Discontinuous at x = 1/2

Question

Let f: R → R be defined by \(f(x) = \begin{cases} x & \quad \text{} x \text{ is irrational}\\ 1- x & \quad \text{} x\text{ is rational} \end{cases}\) then f is …

(a) Discontinuous at x = 1/2

(b) Continuous at x = 1/2

(c) Continuous everywhere 

(d) Discontinuous everywhere

Answer 1

(b) Continuous at x = 1/2