To determine [tex]\( f(5) \)[/tex], we need to find the appropriate piece of the piecewise function that corresponds to [tex]\( x = 5 \)[/tex].
The function is defined as follows:
[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]
1. Identify which piece applies for [tex]\( x = 5 \)[/tex]:
We note that [tex]\( x = 5 \)[/tex] falls into the third case since [tex]\( 5 \geq 4 \)[/tex].
2. Apply the appropriate expression:
Here, [tex]\( f(x) = 5x + 4 \)[/tex] when [tex]\( x \geq 4 \)[/tex].
3. Substitute [tex]\( x = 5 \)[/tex] into the expression:
[tex]\[ f(5) = 5(5) + 4 \][/tex]
4. Perform the calculation:
[tex]\[ f(5) = 25 + 4 = 29 \][/tex]
So, the function value [tex]\( f(5) \)[/tex] is [tex]\( 29 \)[/tex].
Thus, the correct answer is:
[tex]\[ \boxed{29} \][/tex]
