Question

1. let y = f(x) = \

$$\begin{cases} 1 - 5x, & x < -5 \\\\ 3 - x^3, & -5 \\leq x < -2 \\\\ 5 - x^2, & x \\geq -2 \\end{cases}$$

find f(-2)
a. f(-2) = -5
b. f(-2) = 1
c. f(-2) = 9
d. f(-2) = 11

Explanation:

Step1: Identify correct function branch

We need $x=-2$. Check the piecewise function domains: $x \geq -2$ corresponds to $f(x)=5-x^2$.

Step2: Substitute $x=-2$ into the function

Substitute $x=-2$ into $f(x)=5-x^2$.

$$\begin{align*} f(-2)&=5-(-2)^2\\ &=5-4\\ &=1 \end{align*}$$

Answer:

B. $f(-2)=1$