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.

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.

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Answer 2

Samantha Adkison

The function f(x) = (x - 2) / (x^2 - 3x + 2) has a removable discontinuity at x = 2 and a non-removable discontinuity at x = 1.

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Answer from HIX Tutor

When evaluating a one-sided limit, you need to be careful when a quantity is approaching zero since its sign is different depending on which way it is approaching zero from. Let us look at some examples.