Consider the function .

MATHEMATICS · Multi-part · AP · AP Precalculus · Polynomial and Rational Functions · Polynomial and Rational Functions

Problem

Consider the function f(x)=x2−4x2−5x+6f(x)=\dfrac{x^{2}-4}{x^{2}-5x+6}. (i) Find the domain of ff. (ii) List all points where ff is discontinuous. (iii) For each such point, determine whether the discontinuity is removable or non-removable, showing all algebraic working and relevant limits.

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