Marshall Watson
03/08/2023 · High School
Evaluate the piecewise function *
If \( f(x)=\left\{\begin{array}{ll}(x+4)^{2}, & -20 \leq x \leq 0 \\ 3 x^{2}-x & , 0
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Step-by-step Solution
To evaluate the piecewise function \( f(x) \) at \( x = -11 \), we first need to determine which piece of the function applies to this value of \( x \).
The function is defined as follows:
\[
f(x) =
\begin{cases}
(x+4)^{2}, & -20 \leq x \leq 0 \\
3x^{2} - x, & 0 < x \leq 20
\end{cases}
\]
Since \( -11 \) falls within the interval \( -20 \leq x \leq 0 \), we will use the first piece of the function:
\[
f(x) = (x + 4)^{2}
\]
Now, we substitute \( x = -11 \) into this expression:
\[
f(-11) = (-11 + 4)^{2}
\]
Calculating inside the parentheses:
\[
-11 + 4 = -7
\]
Now we square this result:
\[
f(-11) = (-7)^{2} = 49
\]
Thus, the value of \( f(-11) \) is
\[
\boxed{49}
\]
Quick Answer
\( f(-11) = 49 \)
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