The function `f(x)=(4-x^2)/(4x-x^3)` a)discontinuous at only one point b) discontinuous exactly at two points c)discontinuous exactly at three points d) none of these

Explanation

To determine the points of discontinuity for the function \( f(x) = \frac{4 - x^2}{4x - x^3} \), we will analyze the function step by step.

### Step 1: Identify the points of discontinuity
The function \( f(x) \) is a rational function, and it will be discontinuous where the denominator is equal to zero. Therefore, we need to find the values of \( x \) that make the denominator \( 4x - x^3 \) equal to zero.

### Step 2: Set the denominator to zero
We set the denominator equal to zero:
\[
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