Question

The function $f(x)=[x]\cdot \cos\left(\frac{2x-1}{2}\pi\right)$ where $[\cdot]$ denotes the greatest integer function, is discontinuous at

• A. all irrational numbers x.
• B. no x.
• C. all integers.
• D. all rational numbers.

Hint:

Calculus Tip: When testing the product of a discontinuous function (like $[x]$) and a continuous function (like $\cos$), if the continuous function evaluates to 0 exactly at the points where the other jumps, the product function becomes perfectly continuous!

Answer 1

The Correct Option is B