Question

find f(5) for this piecewise-defined function.
\\ f(x) = \

$$\begin{cases} -9x - 1 & \\text{if } x < 2 \\\\ -x + 12 & \\text{if } 2 \\leq x \\leq 6 \\\\ 2x + 5 & \\text{if } x > 6 \\end{cases}$$

\\
write your answer as an integer or as a fraction in simplest form.
\\( f(5) = \\) \\(\square\\)

Explanation:

Step1: Determine the applicable piece

Check which interval \( x = 5 \) belongs to. The intervals are \( x < 2 \), \( 2\leq x\leq6 \), and \( x > 6 \). Since \( 2\leq5\leq6 \), we use the piece \( f(x)=-x + 12 \).

Step2: Substitute \( x = 5 \) into the function

Substitute \( x = 5 \) into \( f(x)=-x + 12 \). So \( f(5)=-5 + 12 \).

Step3: Calculate the result

Simplify \( -5 + 12 = 7 \).

Answer:

\( 7 \)