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The Function F ( X ) = 4 − X 2 4 X − X 3 (A) Discontinuous at Only One Point (B) Discontinuous Exactly at Two Points (C) Discontinuous Exactly at Three Points (D) None of These - Mathematics

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Question

The function 

\[f\left( x \right) = \frac{4 - x^2}{4x - x^3}\]

 

Options

  • discontinuous at only one point

  • discontinuous exactly at two points

  • discontinuous exactly at three points

  • none of these

MCQ
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Solution

 discontinuous exactly at three points 

Given:

\[f\left( x \right) = \frac{4 - x^2}{4x - x^3}\]

  \[\Rightarrow f\left( x \right) = \frac{4 - x^2}{x\left( 4 - x^2 \right)}\]

\[\Rightarrow f\left( x \right) = \frac{1}{x}, x \neq 0 \text{ and }  4 - x^2 \neq 0 \text{ or } x \neq 0, \pm 2\]

Clearly,

\[f\left( x \right)\]  is defined and continuous for all real numbers except \[\left\{ 0, \pm 2 \right\}\] .

Therefore, 

\[f\left( x \right)\]  is discontinuous exactly at three points.
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Chapter 9: Continuity - Exercise 9.4 [Page 42]

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RD Sharma Mathematics [English] Class 12
Chapter 9 Continuity
Exercise 9.4 | Q 1 | Page 42

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