Consider the function .

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

Problem

Consider the function

g(x)=\dfrac{x^{2}-1}{x^{3}-6x^{2}+11x-6}

. (i) Show that

x=1

is a root of the denominator

x^{3}-6x^{2}+11x-6

. (ii) Factor the denominator completely and list all its real zeros. (iii) Hence state the domain of

g(x)

, giving reasons for every exclusion.