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  4. The function f (x)=(4-4x2/4x-x3) is

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Q. The function $f \left(x\right)=\frac{4-4x^{2}}{4x-x^{3}}$ is

Continuity and Differentiability

Solution:

$f \left(x\right)=\frac{4-4x^{2}}{4x-x^{3}}$
$=\frac{4-x^{2}}{x\left(2-x\right)\left(2+x\right)}$
So, $f(x)$ is discontinuous at $x = 0$, $2$, $-2$.