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Determine [tex]f(5)[/tex] for [tex]f(x)=\left\{\begin{array}{ll}x^3, & x\ \textless \ -3 \\ 2x^2-9, & -3 \leq x\ \textless \ 4 \\ 5x+4, & x \geq 4\end{array}\right.[/tex]

A. 11
B. 29
C. 41
D. 125


Sagot :

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]
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