The domain of definition of the function
`f(x)= sin^(-1){log_(2)((x^(2))/(2))}`, is

Answer

To find the domain of the function \( f(x) = \sin^{-1}\left(\log_2\left(\frac{x^2}{2}\right)\right) \), we need to ensure that the argument of the inverse sine function lies within its valid range. The domain of the function \( \sin^{-1}(x) \) is \( -1 \leq x \leq 1 \).

### Step 1: Set up the inequality
We start by setting the argument of the sine inverse function within the required range:
\[ -1 \leq \log_2\left(\frac{x^2}{2}\right) \leq 1 \]

### Step 2: Solve the left inequality
First, we solve the left part of the inequality:
\[ \log_2\left(\frac{x^2}{2}\right) \geq -1 \]
To eliminate the logarithm, we exponentiate both sides with base 2:
\[ \frac{x^2}{2} \geq 2^{-1} \]
This simplifies to:
\[ \frac{x^2}{2} \geq \frac{1}{2} \]
Multiplying both sides by 2 gives:
\[ x^2 \geq 1 \]

### Step 3: Solve the right inequality
Now we solve the right part of the inequality:
\[ \log_2\left(\frac{x^2}{2}\right) \leq 1 \]
Exponentiating both sides with base 2 gives:
\[ \frac{x^2}{2} \leq 2^1 \]
This simplifies to:
\[ \frac{x^2}{2} \leq 2 \]
Multiplying both sides by 2 gives:
\[ x^2 \leq 4 \]

### Step 4: Combine the inequalities
Now we combine the two inequalities:
\[ 1 \leq x^2 \leq 4 \]

### Step 5: Solve for \( x \)
Taking the square root of the inequalities, we get:
\[ 1 \leq |x| \leq 2 \]
This means:
\[ |x| \geq 1 \quad \text{and} \quad |x| \leq 2 \]
This leads to two intervals:
\[ x \leq -1 \quad \text{or} \quad x \geq 1 \]
And also:
\[ -2 \leq x \leq 2 \]

### Step 6: Determine the final intervals
Combining these results, we find:
\[ x \in [-2, -1] \cup [1, 2] \]

### Final Answer
Thus, the domain of the function \( f(x) \) is:
\[ \boxed{[-2, -1] \cup [1, 2]} \]