Question

What is the domain of f(x) = log(x + 1) + 4?

Answer 1

The domain is all the numbers that you are able to use in the function to get a real value
You'd want to look at the functions that can possibly have values that its not defined for, like square roots and denominators of fractions.

Answer 2

for domain the argument of log cannot be less than or equal to 0

so domain will be x belongs to (-1,infinity)