Mathematics

Problem

The denominator of the rational function

g_k(x)=\frac{x^2-1}{x^2-(k+1)x+k}

depends on a real parameter

k

. (i) Determine all real values of

k

for which

g_k

is undefined at exactly one real number. (ii) For each such

k

, write the domain of

g_k

in interval notation.