Question:
If $f(x)=[x]-\left[\frac{x}{4}\right], x \in \mathrm{R}$, where $[x]$ denotes the greatest integer function, then:
Correct Option: 1
Solution:
L.H.L. $\lim _{x \rightarrow 4^{-}}\left([x]-\left[\frac{x}{4}\right]\right)=3-0=3$
R.H.L. $\lim _{x \rightarrow 4^{+}}[x]-\left[\frac{x}{4}\right]=4-1=3$
$f(4)=[4]-\left[\frac{4}{4}\right]=4-1=3$
$\because \mathrm{LHL}=f(4)=\mathrm{RHL}$
$\therefore \mathrm{f}(\mathrm{x})$ is continuous at $\mathrm{x}=4$
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