QuestionQ18) Find the values of $(x)$ which $f(x)=\frac{x-3}{|x|-3}$ that not continuous and determine whether discontinuity is removable? a)3 b) -3 c) 0 d) $\{3,-3\}$

Studdy Solution
Determine if the discontinuities are removable.
At $x = 3$, the left-hand limit and right-hand limit are both 1, but the function is not defined at $x = 3$. Therefore, the discontinuity at $x = 3$ is removable.
At $x = -3$, the left-hand limit and right-hand limit are both -1, but the function is not defined at $x = -3$. Therefore, the discontinuity at $x = -3$ is removable.
The values of $x$ where $f(x)$ is not continuous are $\{3, -3\}$, and both discontinuities are removable.
The correct answer is $\boxed{\{3, -3\}}$.