The function `f(x) = (4-x^(2))/(4x-x^(3))` is discontinuous at

Options

A. discontinuous at only one point
B. discontinuous at exactly two points
C. discontinuous at exactly three points
D. None of the above

Answer

C

Explanation

We have, `f(x) = (4-x^(2))/(4x-x^(2))=((4-x^(2)))/(x(4-x^(2)))`
` = ((4-x^(2)))/(x(2^(2)-x^(2))) = (4-x^(2))/(x(2+x)(2-x))`
Clearly , `f(x)` is discontinuous at exactly three points `x = 0, x = - 2` and `x = 2`.