+816 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!
+128474 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 ???
