Let h_k(x)= x^2+kx+1 x^2-(k+3)x+2k

MATHEMATICS · Subjective · AP · AP Precalculus · Polynomial and Rational Functions · Polynomial and Rational Functions

Problem

Let

h_k(x)=\frac{x^2+kx+1}{x^2-(k+3)x+2k},\qquad k\in\mathbb R.

(a) Find all real values of

x

(in terms of

k

) that make

h_k

undefined, and hence write the domain of

h_k

. (b) Determine the set of all real

k

for which the domain of

h_k

\mathbb R\setminus\{3\}

. (c) Find every real

k

for which

h_k

is defined for all real numbers.