To find the domain of the function $f(x) = \sqrt{4x - 28}$, we need to ensure that the expression inside the square root, $4x - 28$, is non-negative. This is because the square root of a negative number is undefined in the real number system.

Step 1: Set the expression inside the square root greater than or equal to zero:

$4x - 28 \geq 0$

Step 2: Solve the inequality:

$4x \geq 28$ $x \geq \frac{28}{4}$ $x \geq 7$

Step 3: Conclusion

The domain of $f(x)$ is all values of $x$ such that $x \geq 7$.

So, the domain is: $[7, \infty)$

Do you need more details on how to find domains for other types of functions?

Here are some related questions:

1. How do you find the domain of a rational function?
2. How do you handle square roots with expressions other than polynomials?
3. What is the range of the function $f(x) = \sqrt{4x - 28}$?
4. How would you handle a square root of a fraction?
5. How do inequalities in the domain affect the graph of a function?

Tip: Always check the conditions inside square roots and denominators to ensure you're working with valid values.