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

Options

A. discontinuous at only one point
B. discontinuous at extactly 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)-y^(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, because at these points function is not defined.