The domain of the function `f(x)=sqrt(x^(2))` is :

Options

A. `-ooltxltoo`
B. `0ltxltoo`
C. `R-{0}`
D. `0lexltoo`

Answer

To find the domain of the function \( f(x) = \sqrt{x^2} \), we need to determine the set of all possible values of \( x \) for which the function is defined.

### Step-by-Step Solution:

1. **Understand the Function**: The function is given as \( f(x) = \sqrt{x^2} \). The expression inside the square root is \( x^2 \).

2. **Identify the Condition for the Square Root**: The square root function is defined for non-negative values. Therefore, we need to ensure that the expression inside the square root is greater than or equal to zero:
\[ x^2 \geq 0 \]

3. **Analyze the Expression \( x^2 \)**: The square of any real number \( x \) (whether positive or negative) is always non-negative. This means:
- If \( x > 0 \), then \( x^2 > 0 \).
- If \( x < 0 \), then \( x^2 > 0 \).
- If \( x = 0 \), then \( x^2 = 0 \).

4. **Conclusion About the Domain**: Since \( x^2 \) is always greater than or equal to zero for all real numbers \( x \), the function \( f(x) = \sqrt{x^2} \) is defined for all real numbers. Thus, the domain of the function is:
\[ \text{Domain} = (-\infty, \infty) \]

### Final Answer:
The domain of the function \( f(x) = \sqrt{x^2} \) is \( (-\infty, \infty) \).