Question

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\\(g(x) = \

$$\begin{cases} x^2 - 5 &, \\ x \\in (-\\infty, -7) \\\\ 9x - 17 &, \\ x \\in -7, 2 \\\\ (x + 1)(x - 5) &, \\ x \\in (2, \\infty) \\end{cases}$$

\\)
\\(g(7) = \boxed{\space}\\)

Explanation:

Step1: Identify the correct piece

Since $7 \in (2, \infty)$, use $g(x)=(x+1)(x-5)$.

Step2: Substitute $x=7$ into the formula

$g(7)=(7+1)(7-5)$

Step3: Calculate the result

First compute inside the parentheses: $7+1=8$, $7-5=2$. Then multiply: $8 \times 2 = 16$.

Answer:

16