To find [tex]\( f(9) \)[/tex] for the given piecewise function, let's follow these steps:
The piecewise function is defined as:
[tex]\[
f(x) =
\begin{cases}
\frac{2}{5} x + 8 & \text{if } x \leq 5 \\
-x + 15 & \text{if } x > 5
\end{cases}
\][/tex]
We are asked to find [tex]\( f(9) \)[/tex].
1. First, determine which part of the piecewise function applies for [tex]\( x = 9 \)[/tex].
Since [tex]\( 9 > 5 \)[/tex], we will use the second part of the piecewise function:
[tex]\[
f(x) = -x + 15
\][/tex]
2. Substitute [tex]\( x = 9 \)[/tex] into the equation:
[tex]\[
f(9) = -9 + 15
\][/tex]
3. Perform the calculation:
[tex]\[
f(9) = -9 + 15 = 6
\][/tex]
Thus, the value of [tex]\( f(9) \)[/tex] is [tex]\( 6 \)[/tex].
