The domain of the function `f(x)=sqrt(3x-4)` is :

Options

A. `[0, oo)`
B. `[(3)/(4),oo)`
C. `[(4)/(3),oo)`
D. `(4,oo)`

Answer

To find the domain of the function \( f(x) = \sqrt{3x - 4} \), we need to determine the values of \( x \) for which the expression under the square root is non-negative (since the square root of a negative number is not defined in the set of real numbers).

### Step 1: Set the expression inside the square root greater than or equal to zero.
We start by setting up the inequality:
\[ 3x - 4 \geq 0 \]

### Step 2: Solve the inequality for \( x \).
To solve for \( x \), we first add 4 to both sides:
\[ 3x \geq 4 \]
Next, we divide both sides by 3:
\[ x \geq \frac{4}{3} \]

### Step 3: Write the domain in interval notation.
The solution \( x \geq \frac{4}{3} \) indicates that \( x \) can take any value starting from \( \frac{4}{3} \) and going to infinity. Therefore, the domain of the function in interval notation is:
\[ \left[ \frac{4}{3}, \infty \right) \]

### Conclusion:
Thus, the domain of the function \( f(x) = \sqrt{3x - 4} \) is:
\[ \left[ \frac{4}{3}, \infty \right) \]