https://file.aiquickdraw.com/mathbot/file/1728283034327nnqwzjo3.jpg

Misalhen F (x) = VI - 101
dan 9ry)=1-x
Tentrken domain fungsi h (X) = ( E) (X)
G

The problem in the image is asking for the domain of the function \( h(x) \), which is defined as a quotient of two functions:

\[ F(x) = \sqrt{2 - |x|} \quad \text{and} \quad G(x) = 1 - x \]
\[ h(x) = \frac{F(x)}{G(x)} \]

### To determine the domain of \( h(x) \), we need to consider two things:
1. The domain of \( F(x) \), which involves a square root.
2. The domain of \( G(x) \), which involves a potential division by zero.

### 1. Domain of \( F(x) = \sqrt{2 - |x|} \):
- For the square root function to be defined, the expression inside the square root must be non-negative:
  \[
  2 - |x| \geq 0
  \]
  Solving this inequality:
  \[
  |x| \leq 2
  \]
  Which means \( x \in [-2, 2] \). So, the domain of \( F(x) \) is \( x \in [-2, 2] \).

### 2. Domain of \( G(x) = 1 - x \):
- The only restriction for \( G(x) \) comes from the fact that it cannot be zero (since division by zero is undefined):
  \[
  1 - x \neq 0 \quad \Rightarrow \quad x \neq 1
  \]

### Combining both conditions:
- The domain of \( F(x) \) is \( [-2, 2] \), and the function \( G(x) \) excludes \( x = 1 \).
- Therefore, the domain of \( h(x) = \frac{F(x)}{G(x)} \) is:
  \[
  x \in [-2, 2] \setminus \{1\}
  \]
  Which means the domain is \( x \in [-2, 1) \cup (1, 2] \).

### Final Answer:
The domain of \( h(x) \) is \( (-2, 1) \cup (1, 2) \).

Would you like further details or have any questions about this?

Here are 5 related questions for further exploration:
1. What is the range of the function \( F(x) = \sqrt{2 - |x|} \)?
2. How does the absolute value function affect the domain of \( F(x) \)?
3. How would the domain change if \( G(x) = x^2 - 1 \)?
4. What happens to the domain if we modify \( F(x) \) to \( \sqrt{3 - |x|} \)?
5. Can you graph the function \( h(x) \) and verify the domain visually?

**Tip:** Always check for restrictions like square roots or division when finding domains of functions.

Misalkan F(x) = √(2 - |x|) dan G(x) = 1 - x. Tentukan domain fungsi h(x) = F(x)/G(x).

Learn how to find the domain of the function h(x) = F(x)/G(x) where F(x) = √(2 - |x|) and G(x) = 1 - x. This problem involves determining restrictions from square roots and divisions. Ideal for high school students in Grades 10-12.

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