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JEE PYQ: Continuity And Differentiability Question 8

Question 8 - 2021 (24 Feb Shift 1)

If $f : R \to R$ is a function defined by $f(x) = [x - 1] \cos\left(\dfrac{2x - 1}{2}\right)\pi$, where $[\cdot]$ denotes the greatest integer function, then $f$ is:

(1) discontinuous only at $x = 1$

(2) discontinuous at all integral values of $x$ except at $x = 1$

(3) continuous only at $x = 1$

(4) continuous for every real $x$

Show Answer

Answer: (4)


Learning Progress: Step 8 of 36 in this series