The domain of the function f(x)=`abssqrtx` is :

Options

A. `x in(-oo,+oo)`
B. `x in(0,oo)`
C. `xin(9,16)`
D. `x in[0,infty]`

Answer

To find the domain of the function \( f(x) = \text{abs}(\sqrt{x}) \), we need to determine the values of \( x \) for which the function is defined.

### Step-by-Step Solution:

1. **Understand the Function**: The function is defined as \( f(x) = \text{abs}(\sqrt{x}) \). The square root function \( \sqrt{x} \) is only defined for non-negative values of \( x \) (i.e., \( x \geq 0 \)).

2. **Identify Restrictions from the Square Root**:
- The expression \( \sqrt{x} \) requires \( x \) to be greater than or equal to 0. If \( x < 0 \), the square root of a negative number is not defined in the real number system.

3. **Consider the Absolute Value**:
- The absolute value function \( \text{abs}(y) \) is defined for all real numbers \( y \). However, since we are taking the absolute value of \( \sqrt{x} \), we only need to consider the values of \( x \) that make \( \sqrt{x} \) valid.

4. **Combine the Conditions**:
- Since \( \sqrt{x} \) is defined for \( x \geq 0 \) and the absolute value does not impose any additional restrictions, the domain of \( f(x) \) is simply the set of all \( x \) such that \( x \geq 0 \).

5. **Express the Domain**:
- In interval notation, the domain can be expressed as \( [0, \infty) \). This indicates that \( x \) can take any value from 0 to positive infinity, including 0 itself.

### Final Answer:
The domain of the function \( f(x) = \text{abs}(\sqrt{x}) \) is \( [0, \infty) \).

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