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Let $f,g:\mathbb{R}\to\mathbb{R}$ denote the functions

$f(x)=\begin{cases}-x+3,&x\leq 1,\\-ax^2,&\text{otherwise}.\end{cases}$ $g(x)=\begin{cases}\frac{x^3+x^2-x-1}{x-1},&x\neq 1,\\-b,&\text{otherwise}.\end{cases}$

Determine parameters $a,b\in\mathbb{R}$ such that $f$ and $g$ are continuous.

I was thinking about comparing limits for both sides, that is finding $a$ via

$\lim\limits_{x\to 1}-x+3=\lim\limits_{x\to 1}-ax^2$

and $b=-4$ with the same approach. Actually it looked obvious to me that $a=-2$, however my thoughts don't comply with the solution of WolframAlpha. What am I doing wrong here?

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    @martini: Oh again$a$typo... but nevertheless thanks.2012-11-10

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Yes, $a=-2$ and $b=-4$.

Of course, $f$ and $g$ are continuous in the given point if the left and right limits there exist and coincide, and the plot of Wolfram also confirms this (though the text itself 'Discontinuity at $x=1$' is really misleading).