If f(x) = (4-x²)/(4x-x³) then the function is:

If $f(x) = \frac{4-x^2}{4x-x^3}$ then the function is:

(a)discontinuous at only one point.
(b)discontinuous at exactly two points.
(c)discontinuous at exactly three points.
(d)discontinuous at exactly four points.

Answer

Correct option: (c)

Answer: (c) discontinuous at exactly three points. $f(x) = \frac{4-x^2}{x(4-x^2)} = \frac{4-x^2}{x(2-x)(2+x)}$ is undefined where the denominator is $0$, that is at $x = 0, 2, -2$. Hence $f$ is discontinuous at exactly three points.