A lovely function problem

Algebra Level 5

A function \(f:\mathbb{R} -\{a_1,a_2\} \to \mathbb{R},\) where \(\mathbb{R}\) is the set of Real numbers, is defined by \[f(x)=\frac{Ax^2+6x-8}{A+6x-8x^2}\] How many integral values of \(A\) exist for which \(f(x)\) is onto?


Details : \(a_1,a_2\) are the roots of the quadratic equation \(A+6x-8x^2=0\).

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