Given function \(f(x) = \begin{cases} (x^3-x^2+ 2x -2) , & \quad \text{if } x≠1; \text{}\\ 4, & \quad \text{if } x=1\text{} \end{cases}\)
= 1 – 1 + 2 – 2
= 0
Also, f(1) = 4
As we can see that,
\(\lim\limits_{x \to 1^-}\) f(x) = \(\lim\limits_{x \to 1^+}\) f(x)≠f(1)
Therefore,
f(x) is not continuous at x = 1