a) (−∞, 0) U (0, 1] (I think the U means "or")b) All reals except 0 c) (0,∞) d) (−∞, 1)e) (−1, 1)To find the answer I tried to make sure that the number under the square root does not equal a negative number (by this x is less than or equal to 1) With x^-1, I know x can be any number but zero. So x = 1 or x is less than 0(which is minus infinity)So x = (1, −∞)This is answer d, but the answer sheet says that the answer is a). Can you please explain why?. Created by Y. science-mathematics-en - mathematics-en

Your answer was right, x<0 and x=1 is the domain. The representation however is a, which shows the union of these two conditions. (−∞, 0) specifies that x<0 and (0, 1] specifies that x can be 1 but not 0 . If you pick d, you are assuming the domain is continuous from (−∞, 1), which includes 0. You would also be assuming that x can't be 1, when it actually can. Since x can't be 0 and can be 1, you can't consider d as the answer.