We need to determine the domain of the function:

$f(x) = \sqrt{x} + \sqrt{4 - x}$

Step 1: Analyze the conditions for the square roots.

• The square root function is only defined for non-negative numbers. Therefore, we need to ensure that both $\sqrt{x}$ and $\sqrt{4 - x}$ are defined and non-negative.

Condition 1: For $\sqrt{x}$ to be defined:

$x \geq 0$

Condition 2: For $\sqrt{4 - x}$ to be defined:

$4 - x \geq 0$ Solving this inequality: $x \leq 4$

Step 2: Combine the conditions.

From Condition 1, we have $x \geq 0$, and from Condition 2, we have $x \leq 4$.

Thus, the domain is the interval where both conditions are satisfied: $0 \leq x \leq 4$

Step 3: Express the domain in interval notation.

The domain is: $[0, 4]$

Let me know if you want more details or have any questions!

Here are some related questions:

1. How do you handle square root functions in equations?
2. What is the domain of $\sqrt{9 - x^2}$?
3. How do you find the domain of a rational function?
4. How do square roots behave in inequalities?
5. What is the difference between a function's domain and its range?

Tip: When working with square roots, always check if the expression inside the root is non-negative.