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I am comfortable when I am asked to calculate the range of a rational function, but how do we do the reverse? I came across this problem.

If $$f(x)= \frac{x^2 + x + c}{x^2 + 2x + c}$$ then find the value of $c$ for which the range of $f(x)$ does not contain $[-1, -\frac{1}{3}]$.

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