If f(x)=[x]-[ x4], xR, where [x] denotes the greatest integer function, then:

Question

If $f(x)=[x]-\left[\dfrac x4\right]$, $x\in\mathbb{R}$, where $[x]$ denotes the greatest integer function, then:

Accepted Answer

LHL $=3-0=3$; RHL $=4-1=3$; $f(4)=4-1=3$. Since LHL $=$ RHL $=f(4)$, $f$ is continuous at $x=4$.

Solutions · 1