Find the interval of c for which fx-x2-2 x-c -x2-4 x-c attains any real value

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Method of Intervals

Find the inte...

Question

Find the interval of c for which f(x) =(x²+2x+c)/(x²+4x+c) attains any real value

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f : R \to R, f (x) = \frac{x^{2} + 2 x + c}{x^{2} + 4 x + c}

x

\frac{x^{2} + 2 x + c}{x^{2} + 4 x + 3 c}

f (x) = x^{2} + 6 x + a, g (x) = x^{2} + 4 x + b, h (x) = x^{2} + 14 x + c

f (x) = \sqrt{x^{2} - 4}

c

F (x) = \frac{x^{2} - 4 x}{x + 2} [0, 4]

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