The number of points where the function
$$f(x) = \left\{ {\matrix{ {|2{x^2} - 3x - 7|} & {if} & {x \le - 1} \cr {[4{x^2} - 1]} & {if} & { - 1 < x < 1} \cr {|x + 1| + |x - 2|} & {if} & {x \ge 1} \cr } } \right.$$
[t] denotes the greatest integer $\le$ t, is discontinuous is _____________.
Answer (integer)
7
Solution
$\because f(-1)=2$ and $f(1)=3$
<br/><br/>
For $x \in(-1,1),\left(4 x^{2}-1\right) \in[-1,3)$
<br/><br/>
hence $f(x)$ will be discontinuous at $x=1$ and also
<br/><br/>
whenever $4 x^{2}-1=0,1$ or 2
<br/><br/>
$$
\Rightarrow x=\pm \frac{1}{2}, \pm \frac{1}{\sqrt{2}} \text { and } \pm \frac{\sqrt{3}}{2}
$$
<br/><br/>
So there are total 7 points of discontinuity.
About this question
Subject: Mathematics · Chapter: Limits, Continuity and Differentiability · Topic: Limits and Standard Results
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