Certainly! Let's dive into the details of solving the problem. We are given a linear function \( f(x) = -\frac{1}{2}x + 3 \) and need to find the value of \( f(x) \) for a specific \( x \).
### Problem Statement
Find the value of \( f(x) \) when \( x = 4 \).
### Step-by-Step Solution
1. Identify the function:
We are given the function \( f(x) = -\frac{1}{2}x + 3 \).
2. Substitute the given value of \( x \) into the function:
We need to find \( f(4) \). So, we substitute \( x = 4 \) into the function.
3. Follow through with the substitution:
[tex]\[
f(4) = -\frac{1}{2}(4) + 3
\][/tex]
4. Simplify the expression:
Calculate \(-\frac{1}{2}(4)\):
[tex]\[
-\frac{1}{2}(4) = -2
\][/tex]
Now add the constant term:
[tex]\[
-2 + 3 = 1
\][/tex]
5. Write down the final result:
Thus, \( f(4) = 1 \).
### Summary
By substituting \( x = 4 \) into the function \( f(x) = -\frac{1}{2}x + 3 \), we find that \( f(4) = 1 \).
So the value is [tex]\( \boxed{1} \)[/tex].
