1. There is no "h" in f(x) = log(x). The question is nonsense.
2. The log function is defined for arguments greater than zero. You're probably expected to select D, though A and B could also be correct.
3. Same deal. The log function is defined for x > -2, but the domain could be restricted to x > 2. You're expected to select FALSE.
4. Same deal. Choose B, though D is also correct.
5. C is the proper choice. (See discussion of the log function, above.)