The function given is:

$f(t) = t + 7$

This is a linear function, meaning it is defined for all real values of $t$. There are no restrictions on the values $t$ can take, as there are no denominators, square roots, or logarithmic expressions in the function that could limit the domain.

Therefore, the domain of $f(t)$ is all real numbers, which in interval notation is:

$\boxed{(-\infty, \infty)}$

Would you like a more detailed explanation of how to handle domains of different types of functions?

Here are some related questions for practice:

1. What is the domain of $f(t) = \frac{1}{t}$?
2. How do you determine the domain of a square root function?
3. What is the domain of $f(t) = \ln(t)$?
4. Can you explain the domain of $f(t) = \sqrt{t-3}$?
5. What is the domain of $f(t) = \frac{t^2 - 1}{t - 2}$?

Tip: Always check for restrictions such as division by zero or negative numbers inside square roots when determining a function's domain.