Question

Find the complete set of values of a such that $\frac{x^2-x}{1-ax}$ attains all real values.

Answer 1

Let $y=\frac{x^2-x}{1-ax}$

y is real for all values of x except for those values at which $(1-ax)=0$

$1-ax=0\Rightarrow x=\frac{1}{a}$

$\therefore y$ is real $\forall xϵR-\left\{\frac{1}{a}\right\}$