Answer:
Hey!
f is continuous at x = 0.
Step-by-step explanation:
(a) If x = 0, then f(0) = -1
(b) [tex] = \overset{ \text{lim}}{ \underset{ x\longrightarrow0}{}}f(x) = \overset{ \text{lim}}{ \underset{ x\longrightarrow0}{}} \frac{ {x}^{2} - 3x + 2}{x - 2} \\ \\ = \overset{ \text{lim}}{ \underset{ x\longrightarrow0}{}} \frac{(x - 2)(x - 1)}{x - 2} = \overset{ \text{lim}}{ \underset{ x\longrightarrow0}{}}(x - 1) = -1[/tex]
(c) [tex]f(0) = \overset{ \text{lim}}{ \underset{ x\longrightarrow0}{}}f(x)[/tex]
Therefore, f is continuous at x = 0
