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Find [tex]\( f(-1) \)[/tex] for the piece-wise function.

[tex]\[
\begin{array}{c}
f(x)=\left\{
\begin{array}{rr}
-x & \text{if } x \leq 0 \\
x & \text{if } x \ \textgreater \ 0
\end{array}
\right. \\
f(-1)=?
\end{array}
\][/tex]

Sagot :

GinnyAnswer
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]
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