To find the value of [tex]\( f(-1) \)[/tex] for the given piecewise function, we need to determine which part of the piecewise function applies when [tex]\( x = -1 \)[/tex].
The piecewise function is defined as:
[tex]\[
f(x) =
\begin{cases}
-2x + 1 & \text{if } x \leq 1 \\
-x + 2 & \text{if } x > 1
\end{cases}
\][/tex]
Since [tex]\( -1 \leq 1 \)[/tex], we use the first part of the piecewise function, which is [tex]\( f(x) = -2x + 1 \)[/tex].
Now, substitute [tex]\( x = -1 \)[/tex] into [tex]\( -2x + 1 \)[/tex]:
[tex]\[
f(-1) = -2(-1) + 1
\][/tex]
Perform the multiplication:
[tex]\[
-2(-1) = 2
\][/tex]
Then, add 1:
[tex]\[
2 + 1 = 3
\][/tex]
Therefore, the value of [tex]\( f(-1) \)[/tex] is:
[tex]\[
f(-1) = 3
\][/tex]
