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If the inverse exists, how do I find the inverse to this function:

$$ f(x)= x^2 - 6x + 11 $$

with $x \le 3$

Stuck at the quadtric formula. I think i have got the right answer which is $x = 3 ± \sqrt{y-2}$ ? But it doesnt seem right.

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    Have you tried the quadratic formula?2012-10-17
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    Why doesn't the answer (which is correct, by the way) seem right?2012-10-17
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    Notice that $ f(x) = (x - 3)^{2} + 2 $ for all $ x \in \mathbb{R} $. Hence, $ f(2) = f(4) $, so $ f: \mathbb{R} \to \mathbb{R} $ is not $ 1 $-$ 1 $. Also, $ f(x) \geq 2 $ for all $ x \in \mathbb{R} $, so $ f: \mathbb{R} \to \mathbb{R} $ is not onto. If, however, we restrict the domain and co-domain of $ f $ appropriately, then an inverse exists. Consider $ f: [3,\infty) \to [2,\infty) $. Then $ f $ is both $ 1 $-$ 1 $ and onto, which yields the existence of $ f^{-1} $.2014-10-03

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