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**+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 ???

CPhill
Aug 28, 2018