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

Options

A. R
B. `R^(+)`
C. `R-{0}`
D. `R^(+)uu{0}`

Answer

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

### Step 1: Identify the condition for the square root function
The square root function \( \sqrt{x} \) is defined only for non-negative values of \( x \). This means that the expression inside the square root must be greater than or equal to zero.

### Step 2: Set up the inequality
To find the domain, we set up the inequality:
\[ x \geq 0 \]

### Step 3: Solve the inequality
The solution to the inequality \( x \geq 0 \) indicates that \( x \) can take any value starting from 0 and extending to positive infinity. Therefore, the values of \( x \) that satisfy this inequality are:
\[ x \in [0, \infty) \]

### Step 4: Write the domain in interval notation
The domain of the function \( f(x) = \sqrt{x} \) can be expressed in interval notation as:
\[ [0, \infty) \]

### Step 5: Alternative representation
Alternatively, we can also express the domain in set notation as:
\[ \{ x \in \mathbb{R} \mid x \geq 0 \} \]

### Final Answer
Thus, the domain of the function \( f(x) = \sqrt{x} \) is:
\[ [0, \infty) \]

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