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

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

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 $C$