We only need to be concerned with things that make the denominators = 0
In the first fraction, x = 64 makes the denominator = 0
In the second, setting the denominator = 0, we have.... x^2 - 64 = 0.......factoring, we have (x - 8)(x + 8) = 0
Setting each factor to 0, gives us x =8 and x = -8......and these are the two values that make the denominator = 0
In the third fraction....setting the denominator = 0 fgives us x^3 - 64 = 0....add 64 to both sides
x^3 = 64.....take the cube root of both sides and we find that x = 4
So 64, -8, 8 and 4 are not in the domain of the function.
We only need to be concerned with things that make the denominators = 0
In the first fraction, x = 64 makes the denominator = 0
In the second, setting the denominator = 0, we have.... x^2 - 64 = 0.......factoring, we have (x - 8)(x + 8) = 0
Setting each factor to 0, gives us x =8 and x = -8......and these are the two values that make the denominator = 0
In the third fraction....setting the denominator = 0 fgives us x^3 - 64 = 0....add 64 to both sides
x^3 = 64.....take the cube root of both sides and we find that x = 4
So 64, -8, 8 and 4 are not in the domain of the function.