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The problem provided asks to determine the domain of the function:

\[
g(x) = \frac{\sqrt{5x - 3}}{2 - 4x}
\]

### Step 1: Conditions for the Square Root
For the square root to be defined, the expression inside must be non-negative:

\[
5x - 3 \geq 0
\]

Solving this inequality:

\[
5x \geq 3 \implies x \geq \frac{3}{5}
\]

### Step 2: Conditions for the Denominator
The denominator must not be zero to avoid division by zero:

\[
2 - 4x \neq 0
\]

Solving this equation:

\[
4x \neq 2 \implies x \neq \frac{1}{2}
\]

### Step 3: Combine Conditions
The domain must satisfy both conditions:
1. \( x \geq \frac{3}{5} \)
2. \( x \neq \frac{1}{2} \)

Since \( \frac{1}{2} < \frac{3}{5} \), this condition is already excluded. Thus, the domain is:

\[
x \geq \frac{3}{5}
\]

So the domain of the function is \( x \in \left[ \frac{3}{5}, \infty \right) \).

Would you like further explanation or details on any step?

### Related Questions:
1. What happens to the function if the square root is negative?
2. How does the denominator affect the domain in rational functions?
3. Can the function be continuous at \( x = \frac{1}{2} \)?
4. What is the domain of a general square root function?
5. How can you graphically interpret the domain restrictions?

#### Tip:
Always check for both the numerator and denominator constraints when dealing with rational functions.

Tentukan domain dari g(x) = √(5x - 3) / (2 - 4x)

Learn how to determine the domain of the function g(x) = √(5x - 3) / (2 - 4x). This problem involves key concepts such as the conditions for square roots and avoiding division by zero in rational functions. Suitable for Grades 10-12.

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