To find [tex]\( f(1) \)[/tex] for the given piecewise function, we need to determine which part of the piecewise function to use based on the value of [tex]\( x = 1 \)[/tex].
The piecewise function is defined as:
[tex]\[
f(x) =
\begin{cases}
-2x + 10 & \text{if } x < 2 \\
\frac{3}{2}x + 3 & \text{if } x \geq 2
\end{cases}
\][/tex]
1. Identify the appropriate piece of the function:
Since [tex]\( x = 1 \)[/tex], and [tex]\( 1 < 2 \)[/tex], we will use the first part of the piecewise function: [tex]\( y = -2x + 10 \)[/tex].
2. Substitute [tex]\( x = 1 \)[/tex] into the function:
[tex]\[
y = -2(1) + 10
\][/tex]
3. Perform the arithmetic operations:
[tex]\[
y = -2 + 10
\][/tex]
[tex]\[
y = 8
\][/tex]
Thus, [tex]\( f(1) = 8 \)[/tex].
