Question

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$f(x) = \

$$\begin{cases} -x - 4 &, \\ x < 3 \\\\ x^2 - 7 &, \\ 3 \\leq x \\leq 10 \\\\ \\dfrac{120}{x} + 5 &, \\ x > 10 \\end{cases}$$

$
$f(4) = \square$
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Explanation:

Step1: Determine the applicable function part

Since \( 3 \leq 4 \leq 10 \), we use the function \( f(x)=x^{2}-7 \).

Step2: Substitute \( x = 4 \) into the function

Substitute \( x = 4 \) into \( f(x)=x^{2}-7 \), we get \( f(4)=4^{2}-7 \).

Step3: Calculate the value

First, calculate \( 4^{2}=16 \), then \( 16 - 7 = 9 \).

Answer:

\( 9 \)