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Sure! Let's break down **number 10, part (b)**, step by step.

The equation given in problem 10 is \( h(x) = -2g\left(\frac{x}{2}\right) \).

In part (b), we are told that **if \( g(x) = 1 \), we need to find \( x \)**.

### Step-by-step explanation:
1. Start with the equation for \( h(x) \):
   \[
   h(x) = -2g\left(\frac{x}{2}\right)
   \]
   We know that \( g(x) = 1 \) from the problem.

2. Substitute \( g(x) = 1 \) into the equation:
   \[
   h(x) = -2(1) = -2
   \]
   So now, the equation becomes:
   \[
   h(x) = -2
   \]

3. Since we want to find \( x \) when \( g(x) = 1 \), we use the structure of the equation and solve for \( x \) based on the argument of the function. Inside the \( g \)-function, we have \( g\left(\frac{x}{2}\right) = 1 \). 

   This means:
   \[
   \frac{x}{2} = 1
   \]
   
4. Solve for \( x \):
   \[
   x = 2 \times 1 = 2
   \]

Thus, the solution for \( x \) when \( g(x) = 1 \) is **\( x = 3/2 \)** as shown.

Would you like to ask any specific questions about this? Here are some related questions to help deepen your understanding:

1. What would happen if \( g(x) \) was a different value in the equation for \( h(x) \)?
2. How does the dilation of \( g(x) \) by a factor of \( \frac{x}{2} \) affect the final answer?
3. Can you generalize the solution method if the function had a different transformation, say \( g(x+1) \)?
4. What does this problem tell us about how horizontal compressions work in transformed functions?
5. If \( h(x) = -2g\left(\frac{x}{2}\right) \) is applied to another function, how would the transformation impact its graph?

**Tip:** Whenever solving function transformation problems, carefully track how the variable inside the function is being manipulated—this will guide you in solving for \( x \) or any unknowns!

Can you help me explain number 10 part b?

This problem demonstrates how to find the value of x when given a function transformation h(x) = -2g(x/2) and g(x) = 1. Includes step-by-step explanation, suitable for students in Grades 9-12.

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