The function $f(x) = 2x + 1$ is a linear function. Linear functions are defined for all real values of $x$ since there are no restrictions like square roots or divisions by zero. Therefore, the domain of this function is all real numbers.

In interval notation, this is expressed as:

Domain: $(-\infty, \infty)$

So, the correct answer is:

d. $(-\infty, \infty)$

Would you like more details or have any questions?

Here are 5 related questions for further understanding:

1. What is the range of the function $f(x) = 2x + 1$?
2. How would the domain change if the function were $f(x) = \frac{1}{2x + 1}$?
3. What is the slope of the function $f(x) = 2x + 1$?
4. How do you graph the function $f(x) = 2x + 1$?
5. What is the inverse of the function $f(x) = 2x + 1$?

Tip: When determining the domain of a function, look for any operations that may restrict the values of $x$, such as square roots, denominators, or logarithms.