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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

Best Answer 

 #2
avatar+30620 
+2

As follows:

 

 Jun 26, 2020
 #1
avatar+110154 
+1

 

 

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

 

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
avatar+30620 
+2
Best Answer

As follows:

 

Alan Jun 26, 2020

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