King Chandler
06/23/2024 · High School
Evaluate the piecewise function *
4) \( f(x)=\left\{\begin{array}{cc}14 & , x \leq 0 \\ x^{2}-9 x & , 0
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Step-by-step Solution
To evaluate the piecewise function \( f(x) \), we will consider the two cases defined in the function.
The function is defined as:
\[
f(x) =
\begin{cases}
14 & , x \leq 0 \\
x^{2} - 9x & , 0 < x < \infty
\end{cases}
\]
i) For \( f(-5) \):
Since \(-5 \leq 0\), we use the first case of the piecewise function:
\[
f(-5) = 14
\]
ii) For \( f(1) \):
Since \(1 > 0\), we use the second case of the piecewise function:
\[
f(1) = 1^{2} - 9 \cdot 1 = 1 - 9 = -8
\]
Thus, the evaluations are:
i) \( f(-5) = 14 \)
ii) \( f(1) = -8 \)
Quick Answer
i) \( f(-5) = 14 \)
ii) \( f(1) = -8 \)
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