Question

2.
$f(x)=\

$$\begin{cases}x^3 - 7x, & x\\leq - 3\\\\8, & - 3 < x\\leq 3\\\\\\sqrt{2x + 3}, & x > 3\\end{cases}$$

$
a. $f(-5) = $
b. $f(11) = $
c. $f(0) = $
d. $f(3) = $

Explanation:

Part a: Step1: Match x=-5 to the correct piece

Since $-5 \leq -3$, use $f(x)=x^3-7x$.

Part a: Step2: Substitute x=-5 into the formula

$$f(-5)=(-5)^3 - 7(-5)$$
$$= -125 + 35$$

Part b: Step1: Match x=11 to the correct piece

Since $11 > 3$, use $f(x)=\sqrt{2x+3}$.

Part b: Step2: Substitute x=11 into the formula

$$f(11)=\sqrt{2(11)+3}$$
$$=\sqrt{22+3}=\sqrt{25}$$

Part c: Step1: Match x=0 to the correct piece

Since $-3 < 0 \leq 3$, use $f(x)=8$.

Part d: Step1: Match x=3 to the correct piece

Since $3 \leq 3$, use $f(x)=8$.

Answer:

a. $f(-5) = -90$
b. $f(11) = 5$
c. $f(0) = 8$
d. $f(3) = 8$