Find the domain of the function. (Enter your answer using interval notation.)
f(x)=√x + √4-x

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.

Find the domain of the function. (Enter your answer using interval notation.) f(x) = √x + √(4 - x)

Learn how to find the domain of the function f(x) = √x + √(4 - x) using square root function properties and inequality solving. This detailed guide helps you determine where the function is defined, perfect for students in Grades 9-12.

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