Investigate the following function $f : \mathbb{R} \to \mathbb{R}$ for removable discontinuities, where $f(−3) = 2, f(0) = 1, f(1) = 0$, and $f(x)=\frac{x^3-2x^2-15x}{x^3-2x^2-3x}$ if $x \in \mathbb{R} \setminus \{−3, 0, 1\}$.
This is the task at hand. I have come up with a solution which is $\frac{x-5}{x-1}$ and that $-3$ and $0$ are removable discontinuities, while $1$ is an essential discontinuity. However I am confused about the description. Does $f(−3) = 2$, $f(0) = 1$, $f(1) = 0$ have to be true for $\frac{x-5}{x-1}$? Because this is obviously not true in all cases and how would I find out where this is true.
