How many real numbers are not in the domain of the function
f(x) = 1/(x - 64) + 1/(x^2 - 64) + 1/(x^3 - 64) + 1/(x^4 - 64)?
+128474 Whatever x makes the denominator = 0 is not in the domain
x - 64 =0
64 is not in the domain
x^2 - 64 = 0 so.... ( x + 8) ( x -8) = 0 ....so x = -8 and x = 8 are not in the domain
x^3 - 64 = 0
x^3 = 64
x = 4 is not in the domain
x^4 - 64 = 0
(x^2 - 8) (x^2 + 8) = 0
x^2 - 8 =0 ⇒ x = ±sqrt (8)
The second factor set to 0 produces a non-real solution
So....not in the domain = x = -8, -sqrt (8) , 4 , sqrt (8), 8 , 64
