Certainly! Let's find [tex]\( f(x) \)[/tex] for [tex]\( x = -4 \)[/tex] using the given piecewise function:
The function is defined as follows:
[tex]\[
f(x) = \begin{cases}
x^2 & \text{if } x \leq 3 \\
2x - 4 & \text{if } x > 3
\end{cases}
\][/tex]
Given [tex]\( x = -4 \)[/tex]:
1. First, we determine which piece of the piecewise function to use. Since [tex]\( -4 \leq 3 \)[/tex], we use the piece of the function where [tex]\( x \leq 3 \)[/tex]:
[tex]\[
f(x) = x^2
\][/tex]
2. Next, substitute [tex]\( x = -4 \)[/tex] into this part of the function:
[tex]\[
f(-4) = (-4)^2
\][/tex]
3. Compute the value:
[tex]\[
(-4)^2 = 16
\][/tex]
So, [tex]\( f(-4) = 16 \)[/tex].
Therefore, the answer is:
[tex]\[
\boxed{16}
\][/tex]
