The domain of definition of the function `f (x) = log|4-x^2| `is R-{2,-2}.

Answer

To find the domain of the function \( f(x) = \log |4 - x^2| \), we need to determine the values of \( x \) for which the function is defined. The logarithmic function is defined only for positive arguments, so we need to ensure that \( |4 - x^2| > 0 \).

### Step-by-Step Solution:

1. **Set the argument of the logarithm greater than zero**:
\[ |4 - x^2| > 0 \]
This means that \( 4 - x^2 \) must not equal zero.

2. **Find when the expression inside the absolute value equals zero**:
\[ 4 - x^2 = 0 \]
Rearranging gives:
\[ x^2 = 4 \]
Taking the square root of both sides, we find:
\[ x = 2 \quad \text{or} \quad x = -2 \]

3. **Identify the points where the function is not defined**:
The points \( x = 2 \) and \( x = -2 \) make the argument of the logarithm zero, which is not allowed. Therefore, these points must be excluded from the domain.

4. **Write the domain**:
The domain of the function is all real numbers except \( 2 \) and \( -2 \):
\[ \text{Domain} = \mathbb{R} \setminus \{2, -2\} \]

### Final Answer:
The domain of the function \( f(x) = \log |4 - x^2| \) is \( \mathbb{R} \setminus \{2, -2\} \).