Consider the function .

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

Problem

Consider the function

f(x)=\dfrac{x+1}{x^2-4}

. (i) Factorise the denominator of

f(x)

. (ii) Explain, without performing any numerical calculation, why the roots obtained in part (i) cannot belong to the domain of

f(x)

. (iii) The function

g(x)=\dfrac{x+1}{x^2-4} \times (x-2)

is formed by multiplying the numerator and denominator of

f(x)

(x-2)

. Discuss whether the set of excluded values changes for

g(x)

compared with

f(x)

and give reasons.