the following problems find the points where given function defined and therefore not continuous. For each such point a, - \( f(x)=\frac{x}{(x+3)^{3}} \) - \( f(x)=\frac{x-2}{x^{2}-4} \)

For the function \( f(x) = \frac{x}{(x+3)^{3}} \), we need to check where the denominator equals zero, as that would make the function undefined. Here, the denominator \( (x + 3)^3 = 0 \) at \( x = -3 \). Since division by zero is undefined, \( f(x) \) is not continuous at this point. In the case of \( f(x) = \frac{x-2}{x^{2}-4} \), this fraction simplifies to \( \frac{x-2}{(x-2)(x+2)} \). We identify that \( x = 2 \) and \( x = -2 \) make the denominator zero, leading to discontinuities. However, \( x = 2 \) is removable since it cancels with the numerator, while \( x = -2 \) is a non-removable discontinuity. Thus, \( f(x) \) is not continuous at \( x = -2 \) and has a removable discontinuity at \( x = 2 \).