I assume by e, you mean exponential to the power of one.
If that is the case, the domain of f(t) is all real numbers, since the value of t will not affect 4.5e, which is a constant.
For g(x) on the other hand, we have a logarithm. Thus, x + 3 must be more than 0.
We have:
x + 3 > 0
x > -3
Hence, the domain of g(x) is all real numbers greater than -3.