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The problem asks to solve for the input when the output is \(-3\), given the function \( f(x) = \frac{1}{2}x - 3 \).

We need to find the value of \(x\) when \(f(x) = -3\).

### Steps:
1. Set the function equal to the output:
   \[
   f(x) = -3
   \]
   \[
   \frac{1}{2}x - 3 = -3
   \]

2. Add 3 to both sides of the equation:
   \[
   \frac{1}{2}x = 0
   \]

3. Multiply both sides by 2 to solve for \(x\):
   \[
   x = 0
   \]

So, the input is \( x = 0 \) when the output is \(-3\).

Would you like a more detailed explanation or have any questions?

Here are some related questions:
1. How do you solve linear equations with fractions?
2. What is the general process for solving \(f(x) = y\)?
3. How do you graph the function \(f(x) = \frac{1}{2}x - 3\)?
4. What does the slope represent in the function \(f(x) = \frac{1}{2}x - 3\)?
5. How can you verify your solution for \(x\) by substitution?

**Tip:** Always isolate the variable by reversing operations step by step to maintain balance in the equation.

Solve y = f(x) for x. Then find the input when the output is -3. The function given is f(x) = (1/2)x - 3.

Learn how to solve for x in the linear function f(x) = (1/2)x - 3 when the output is -3. This problem demonstrates key concepts in algebra, including solving linear equations and understanding function outputs. Suitable for students in Grades 7-9.

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