Question

given functions $f(x)$ and $g(x)$ shown below
$f(x)=\

$$\begin{cases}x^{2}+5, & x\\leq 2 \\\\-3x, & x>2\\end{cases}$$

$
$g(x)=\

$$\begin{cases}5x+7, & x<0 \\\\(x-1)^{2}+2, & 0\\leq x<4 \\\\-x, & x\\geq 4\\end{cases}$$

$
find each of the following:
a. $f(5)=\square$
b. $g(8)=\square$
c. $2f(5)-g(8)=\square$
graphing calculator

Explanation:

Step1: Evaluate $f(5)$

Since $5>2$, use $f(x)=-3x$.
$f(5)=-3\times5=-15$

Step2: Evaluate $g(8)$

Since $8\geq4$, use $g(x)=-x$.
$g(8)=-8$

Step3: Calculate $2f(5)-g(8)$

Substitute the values from Step1 and Step2.
$2f(5)-g(8)=2\times(-15)-(-8)=-30+8=-22$

Answer:

A. $f(5)=-15$
B. $g(8)=-8$
C. $2f(5)-g(8)=-22$