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For what real value of \(N\) does the range of the function \(y = f(x) = \frac{4x^2 + Nx + N}{x + 1}, \), where \(x\) is real (and \(x \neq -1\)) consist of all real numbers except for a single interval of the form \(-L < y < L\)?

 Apr 6, 2019
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\(\dfrac{df}{dx} = 0 \Rightarrow x = -2,~0\\ \text{we want } f(0) = -f(-2) = L\\ f(0) = N\\ f(-2) = N-16\\ N = 16-N\\ N=8 \)

 

\(f(x) \in \mathbb{R} - (-8,8)\)

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 Apr 6, 2019

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