To find [tex]\( f(-1) \)[/tex] for the given piecewise function [tex]\( f(x) \)[/tex], we need to evaluate it based on the specified conditions in the piecewise definition:
[tex]\[
f(x) = \begin{cases}
-x & \text{if } x \leq 0 \\
x & \text{if } x > 0
\end{cases}
\][/tex]
Given that [tex]\( x = -1 \)[/tex]:
1. Determine which condition applies to [tex]\( x = -1 \)[/tex]. Since [tex]\( -1 \leq 0 \)[/tex], we use the first part of the piecewise function [tex]\( -x \)[/tex].
2. Substitute [tex]\( x = -1 \)[/tex] into [tex]\( -x \)[/tex]:
[tex]\[
-(-1) = 1
\][/tex]
Thus, the value of [tex]\( f(-1) \)[/tex] is:
[tex]\[
f(-1) = 1
\][/tex]
Therefore, the answer is:
[tex]\[
f(-1) = 1
\][/tex]
