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The function $f(x)=\Large \frac{4-x^2}{4x-x^3}$ is

\[\begin{array}{1 1}(A) \;discontinuous \;at\; only\; one\;point.\\(B)\;discontinuous\;at\;exactly\;two\;points.\\ (C)\;discontinuous\;at\;exactly \;three\;points.\\(D)\;none\;of\;these\end{array}\]

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Toolbox:
  • A function is said to be discontinuous if the $LHL\neq RHL$
  • A function is said to be discontinuous if either the LHL or RHL does not exist.
$f(x)=\large\frac{4-x^2}{4x-x^2}$
Consider the denominator of the function $4x-x^3$
This is a cubic function,which can have three zeroes .
Hence at three points the function can become discontinuous.
Hence the correct option is $C$
answered Jul 4, 2013 by sreemathi.v
 
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