Consider the rational function f(x)= (x-4)(x+2) (x-4)(x-1)
MATHEMATICS · Subjective · AP · AP Precalculus · Polynomial and Rational Functions · Polynomial and Rational Functions
Problem
Consider the rational function
f(x)=(x−4)(x−1)(x−4)(x+2).
Answer the following questions.
(i) Write f(x) in its simplest algebraic form after cancelling common factors, if any.
(ii) List all real numbers that must be excluded from the domain of f and give a brief reason for each exclusion.
(iii) Even though the simplified form obtained in part (i) no longer shows one of the cancelled factors in its denominator, explain clearly why the corresponding excluded value obtained in part (ii) can still not be included in the domain.
(iv) State the final domain of f using set-builder notation.