# 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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