Q.Let $f(x) = \begin{cases} \dfrac{\sin[\pi x]}{[x]} & x \ne \text{integer} \ 0 & x = \text{integer} \end{cases}$ . Then $f$ is

continuous at every integer

discontinuous at every integer

continuous nowhere

continuous at non-integers only

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⁡[πx][x]x≠integer 0x=integerf(x) = \begin{cases} \dfrac{\sin[\pi x]}{[x]} & x \ne \text{integer} \ 0 & x = \text{integer} \end{cases}f(x)={[x]sin[πx]​​x=integer 0​x=integer​. Then fff is