Let's determine [tex]\( f(-3) \)[/tex] for the piecewise function given by:
[tex]\[
f(x)=
\begin{cases}
x^3 & \text{if } x < -3 \\
2x^2 - 9 & \text{if } -3 \leq x < 4 \\
5x + 4 & \text{if } x \geq 4
\end{cases}
\][/tex]
We are asked to find [tex]\( f(-3) \)[/tex].
1. First, identify which part of the piecewise function to use:
- Since [tex]\(-3\)[/tex] falls within the interval [tex]\([-3, 4)\)[/tex], we use [tex]\( f(x) = 2x^2 - 9 \)[/tex].
2. Substitute [tex]\( x = -3 \)[/tex] into the function [tex]\( 2x^2 - 9 \)[/tex]:
[tex]\[
f(-3) = 2(-3)^2 - 9
\][/tex]
3. Calculate the value step-by-step:
- Calculate [tex]\((-3)^2\)[/tex]:
[tex]\[
(-3)^2 = 9
\][/tex]
- Multiply by 2:
[tex]\[
2 \cdot 9 = 18
\][/tex]
- Subtract 9:
[tex]\[
18 - 9 = 9
\][/tex]
Thus, the value of [tex]\( f(-3) \)[/tex] is [tex]\( 9 \)[/tex].
So, [tex]\( f(-3) = 9 \)[/tex].
