A function $f:R-{a_1,a_2}$ to $R$ 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. I tried finding the range of this function, but I did not find things working out. Please see- This is a problem from brilliant.org(I am not cheating, I have used all my chances).
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Maybe you're not cheating, but are you encouraging others to cheat by coming here to look at the answers you get? – Gerry Myerson Feb 06 '15 at 06:24
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Please see that I am not asking for answers, I liked the answer mathgeek gave. He told me I was going right, but he didn't tell me the answer. I am discussing for different approaches. – Feb 06 '15 at 06:26
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I too solved that problem a couple of days back. You were on the right path, replace $f(x)$ by $y$ , cross multiply, make a quadratic in $x$ and make its $D>0$. Then, you must have a quadratic in $y$. A quadratic is always$>0$, only when its own $D<0$. Then, finally, you would have an expression in $A$, which you must be able to factorize, and with the method of solving inequality(probably the method of intervals), you will have your answer.