Q.Let $f(x) = \begin{cases} \dfrac{\sin(x-[x])}{x-[x]} & x \notin \mathbb{Z} \ 1 & x \in \mathbb{Z} \end{cases}$ . Then $f(x)$ is

continuous everywhere

continuous only at integers

discontinuous at integers

periodic with period 1

The correct solution involves applying the fundamental concept to derive the final value step by step...

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Q.Let f(x)={sin⁡(x−[x])x−[x]x∉Z 1x∈Zf(x) = \begin{cases} \dfrac{\sin(x-[x])}{x-[x]} & x \notin \mathbb{Z} \ 1 & x \in \mathbb{Z} \end{cases}f(x)={x−[x]sin(x−[x])​​x∈/Z 1​x∈Z​. Then f(x)f(x)f(x) is