Find the domain of the real function `f(x)` defined by `f(x)=sqrt((1-|x|)/(2-|x|))dot`

Explanation

To find the domain of the function \( f(x) = \sqrt{\frac{1 - |x|}{2 - |x|}} \), we need to ensure that the expression inside the square root is non-negative and the denominator is not zero. We will consider two cases based on the absolute value of \( x \).

### Step 1: Analyze the function for \( x \geq 0 \)

When \( x \geq 0 \), we have \( |x| = x \). Thus, the function simplifies to:
\[ f(x) = \sqrt{\frac{1 - x}{2 - x}} \]
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