Question

find f(-2) for this piecewise-defined function.
f(x) = \

$$\begin{cases} 4x + 8 & \\text{if } x \\leq -6 \\\\ 9x + 1 & \\text{if } x > -6 \\end{cases}$$

write your answer as an integer or as a fraction in simplest form.
f(-2) = \square

Explanation:

Step1: Determine the applicable piece

Check if \( x = -2 \) satisfies \( x \leq -6 \) or \( x > -6 \). Since \( -2 > -6 \), use \( f(x)=9x + 1 \).

Step2: Substitute \( x = -2 \)

Substitute \( x=-2 \) into \( 9x + 1 \): \( 9(-2)+1=-18 + 1=-17 \).

Answer:

\(-17\)