To find the value of the piecewise function [tex]\( f(x) \)[/tex] at [tex]\( x = 4 \)[/tex], we need to determine which piece of the function to use based on the value of [tex]\( x \)[/tex].
The piecewise function [tex]\( f(x) \)[/tex] is defined as follows:
[tex]\[
f(x) = \begin{cases}
-2x + 1 & \text{if } x \leq 1 \\
-x + 2 & \text{if } x > 1
\end{cases}
\][/tex]
Since [tex]\( x = 4 \)[/tex] is greater than 1, we use the second piece of the function:
[tex]\[
f(x) = -x + 2 \quad \text{for } x > 1
\][/tex]
Next, we substitute [tex]\( x = 4 \)[/tex] into this equation:
[tex]\[
f(4) = -4 + 2
\][/tex]
Perform the calculation:
[tex]\[
-4 + 2 = -2
\][/tex]
Therefore, the value of the function [tex]\( f(4) \)[/tex] is:
[tex]\[
f(4) = -2
\][/tex]
