MATHEMATICS · Multi-part · AP · AP Precalculus · Polynomial and Rational Functions · Polynomial and Rational Functions
Problem
Two students, Asha and Vikram, are discussing the function
h(x)=x−5(x−5)(x+2).
Asha claims that the domain of h is all real numbers because the common factor x−5 cancels out, while Vikram insists that x=5 must still be excluded from the domain.
(i) Explain, with reference to the definition of the domain of a rational function, which student is correct.
(ii) State the correct domain of h(x) and describe in words why this choice is necessary even after simplification.