Domain of a function

Please help me find the domain of this function
(4-x)^(1/2) + (x^2-1)^(1/2)

(-infinity, -1) u [1,4]

Well, you can't have a number larger than 4 because for (4-x)^(1/2), you know you can't have a negative number under the square root. You also can't have 0 because (x^2-1)^(1/2) would be negative, so I'm thinking
(- infinity, -1) (1, 4)

For the first part, x has to be less than or equal to 4. For the second part, x has to be greater than or equal to 1 or less than or equal to negative 1.

Domain: less than or equal to 4.

Both of the radicands must be non-negative.

4 - x ≥ 0
x ≤ 4

x² - 1 ≥ 0
x² ≥ 1
x ≥ 1 or x ≤ -1

x ≤ -1 or 1 ≤ x ≤ 4
(-∞, -1] U [1, 4]

(-∞,0)∪(0, 5)