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# Asymptotes Question

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If

$$f(x) = \frac{2x-8}{x^2 -2x - 3} \qquad\text{ and }\qquad g(x) = \frac{3x+9}{2x-4}$$
What is the horizontal asymptote as $$x$$ approaches negative infinity of $$f(g(x))$$?

Jun 19, 2020
edited by SaltyGrandma  Jun 19, 2020

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As follows:

Jun 26, 2020

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$$f(x) = \frac{2x-8}{x^2 -2x - 3} \qquad\text{ and }\qquad g(x) = \frac{3x+9}{2x-4}$$

I found    $$f( \frac{3x+9}{2x-4})$$       and then I simplified it all down.

There was a lot of algebra and I have not checked my result.  Checking could be done by graphing the original substituted function

anyway I ended up with    [ -40(x^2+....)]  /  [-15(x^2+....) ]   if this is correct I would assume that the horizontal asymptote is

40/15 = 8/3

But there could be 100 mistakes in my working and also in my logic.

Jun 26, 2020
#2
+31103
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