Question

What are the removable and non-removable discontinuities, if any, of `f(x)=(x - 2) / (x^2 - 3x + 2 )`?

Answer 1

`x=2` is a removeable discontinuity and `x=1` is a non-removeable discontinuity.

Explanation:

factorizing the denominator we get

`f(x)=(x-2)/((x-2)(x-1))=(x-2)/(x-1)`.

`therefore x=2` is a removeable discontinuity since the factor `(x-2)` leading to division by zero cancelled out, and `x=1` is a non-removeable discontinuity since it leads to division by zero in the denominator.