Define $f: \mathbb{R} \rightarrow \mathbb{R}$ by $f(x)=[x]+\sqrt{x-[x]}$ for $x \in \mathbb{R}$, where $[x]$…

Define $f: \mathbb{R} \rightarrow \mathbb{R}$ by $f(x)=[x]+\sqrt{x-[x]}$ for $x \in \mathbb{R}$, where $[x]$ denotes the greatest integer function. Then the set of points at which $f$ is continuous is
  1. $\mathbb{R}^{+}$
  2. $\mathbb{R}$
  3. $\mathbb{R}-\mathbb{Z}$
  4. $\{1,2,3, \ldots\}$

Solution

No solution. Refer to answer key.

Asked in: AP EAMCET 2017 (25 Apr Shift 1)

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