Question

If f(x)= begincases sin x, & when x is rational
cos x, & when x is irrational endcases then the function is:

• A. discontinuous at x=nπ+π/4
• B. continuous at x=nπ+π/4
• C. discontinuous at all x
• D. none of these

Hint:

Such functions are continuous only where the two defining expressions coincide.

Answer 1

The Correct Option is A

Step 1: Continuity requires sin x=cos x.
Step 2: sin x=cos x ⟹ x=nπ+(π)/(4)
Step 3: At these points, limits match, otherwise they differ.