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We are given that the domain of the function \( g \) is \( -6 \leq x \leq 12 \), and the function \( h(x) \) is defined as \( h(x) = 3g\left( \frac{x}{2} \right) \).

### Step 1: Find the Domain of \( \frac{x}{2} \)
Since the function \( g \) accepts inputs in the range \( -6 \leq x \leq 12 \), we need to find the range of \( x \) values such that \( \frac{x}{2} \) is within the domain of \( g \), i.e., \( -6 \leq \frac{x}{2} \leq 12 \).

### Step 2: Solve the Inequality
To find the range of \( x \), multiply the inequality by 2 to eliminate the fraction:
\[
-6 \times 2 \leq x \leq 12 \times 2
\]
\[
-12 \leq x \leq 24
\]

### Step 3: Conclusion
The domain of \( h(x) \) is \( -12 \leq x \leq 24 \), which corresponds to option **B**.

Let me know if you would like further details or explanations!

### Related Questions:
1. What is the range of the function \( g(x) \) if its domain is \( -6 \leq x \leq 12 \)?
2. How do transformations like \( g\left(\frac{x}{2}\right) \) affect the domain of a function?
3. What happens to the domain if \( h(x) \) were defined as \( h(x) = g(x^2) \)?
4. How would the answer change if the domain of \( g(x) \) was different?
5. Can a function have more than one valid domain depending on how it is transformed?

### Tip:
Always focus on how transformations (like scaling or shifting) affect the input of the function and adjust the domain accordingly.

The domain of the function g is −6 ≤ x ≤ 12. If the function h is given by h(x) = 3g(x/2), what is the domain of h?

Learn how to find the domain of the function h(x) = 3g(x/2), where the domain of g is −6 ≤ x ≤ 12. This problem involves transformations of functions and inequalities, making it suitable for Grades 10-12 students.

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