Consider the function f (x) = [ . x [x] ; ; ; ; ; ; ; ; ; ; ; ; ;… - Vidyadip

MCQ

Consider the function $f (x) =$$\left[ \begin{gathered} \hfill \\ \hfill \\ \hfill \\ \hfill \\ \hfill \\ \end{gathered} \right.$$\begin{gathered} \frac{x}{{[x]}}\;\;\;\;\;\;\;\;\;\;\;\;\;if\;\;1 \leqslant \;x < 2 \hfill \\ \hfill \\ 1\;\;\;\;\;\;\;\;\;\;\;\;\;\;\;\;if\;\;x = 2 \hfill \\ \hfill \\ \sqrt {6 - x} \;\;\;\;\;\;\;if\;\;2 < x \leqslant 3 \hfill \\ \end{gathered} $

where $[x]$ denotes step up function then at $x = 2$ function

A
has missing point removable discontinuity
✓
has isolated point removable discontinuity
C
has non removable discontinuity finite type
D
is continuous

✓

Answer

Correct option: B.

has isolated point removable discontinuity

b
from the figure the function has an obvious removable isolated point discontinuous.

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