To find the inverse of the function \( g(x) = 8 - \frac{x}{2} \), we follow these steps:

### Step 1: Set \( g(x) = y \)
Let \( y = 8 - \frac{x}{2} \).

### Step 2: Solve for \( x \) in terms of \( y \)
1. Start with the equation: 
   \[
   y = 8 - \frac{x}{2}
   \]
2. Subtract 8 from both sides:
   \[
   y - 8 = -\frac{x}{2}
   \]
3. Multiply both sides by -2 to isolate \( x \):
   \[
   x = -2(y - 8)
   \]
4. Simplify:
   \[
   x = -2y + 16
   \]

### Step 3: Swap \( x \) and \( y \)
Now, swap \( x \) and \( y \) to get the inverse function:
\[
g^{-1}(x) = -2x + 16
\]

Thus, the inverse of the function is:
\[
g^{-1}(x) = -2x + 16
\]

Would you like further details on any steps or how inverse functions work?

Here are 5 related questions:
1. What are the conditions for a function to have an inverse?
2. How do you graph both a function and its inverse?
3. Can every function have an inverse? Why or why not?
4. What is the meaning of an inverse function in real-world contexts?
5. How can you verify that a function and its inverse are correct?

**Tip:** To check if you've found the correct inverse, compose the original function with the inverse. You should get \( x \) as a result.

Learn how to find the inverse of the function g(x) = 8 - x/2 in this detailed step-by-step guide. This problem covers key algebra concepts and includes a full explanation of how to derive the inverse function g^-1(x) = -2x + 16. Suitable for Grades 9-11.

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