Find the domain and range of a quadratic

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$$F(x)=\frac {x^2+ax+1}{x^2+x+1}$$ Find the complete set of values of 'a' such that $F(x)$ is onto And f(x) maps from real numbers to real numbers.

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The domain is when $ x^{2}+x+1 \neq 0 $ And you know that this function is never 0 so you will get your domain: $\mathbb{R}$