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What is the domain of the function  \(f(x)=\frac{x+2}{x^2-2x-24}\)? Express your answer in interval notation. First, I did: x^2-2x-24=0, and got the solutions x=6, x=-4, so the answer is [6,-4], but the answer is wrong! Help!

mathtoo  Aug 28, 2018
 #1
avatar+90969 
+2

f(x)  =        x + 2

           __________

           x^2 - 2x - 24

 

The domain will only be affected by the denominator....[the numerator has a domain of all real numbers]

 

So....when the denominator  = 0 , this function is undefined....so...let's find out what makes the denominator  = 0

 

x^2 - 2x  - 24  = 0    factor

(x - 6) ( x + 4)  =0     set both factors to 0 and solve for x and we  get  x = 6  and  x  = -4

 

Note...you have the right  answers, Mathtoo...we just need to take it a little further

 

We are saying that the domain is all real numers  EXCEPT   -4  and 6

 

So.....the solution is

 

(-infinity, -4 )  U ( - 4, 6)  U  ( 6 , infinity )

 

Do you see  ???

 

cool cool cool

CPhill  Aug 28, 2018
edited by CPhill  Aug 28, 2018
 #2
avatar+621 
+2

Oh, yeah! Domain! That's how you write it! I see! Thank you!

mathtoo  Aug 28, 2018

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