Final answer:
The correct domains where x is one to one are A) x < 0 and B) x > 0 because they prevent a function from mapping multiple values of x to the same value of y, which is not the case for options C and D.
Step-by-step explanation:
The question asks for a domain where x is one to one. To be one to one, each value of x must map to a unique value of y in a function. Given the options:
- A) x < 0
- B) x > 0
- C) All real numbers
- D) x ≠ 0
Both A and B are domains where a function can be one to one because they exclude the possibility of positive and negative values of x producing the same y value. However, option C, which includes all real numbers, might not be one to one if, for example, the function is quadratic because for each positive x there is a negative x that yields the same y value (except for x = 0). Option D, which excludes x = 0, still allows for both positive and negative values of x, which doesn't guarantee a one-to-one relationship. If the function were f(x) = x², for instance, f(2) = 4 and f(-2) = 4, which is not one to one.
Therefore, both A) x < 0 and B) x > 0 can be considered correct as domains where a function would be one to one.