Mathematics

Problem

Let

g_k(x)=\dfrac{1}{x^{2}-kx}

, where

k\in\mathbb R

. a. (i) Express the domain of

g_k

in terms of

k

. b. (ii) Determine all real values of

k

for which the domain of

g_k

excludes exactly two distinct non-zero real numbers. Justify your answer.