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. $f(2)=\square$b. $g(3)=\square$c. $f(2)+g(3)=\square$graphing calculator

Explanation:

Step1: Evaluate $f(2)$

Use $f(x)=x^2+5$ since $2\leq2$

$$\begin{align*} f(2)&=2^2+5\\ &=4+5\\ &=9 \end{align*}$$

Step2: Evaluate $g(3)$

Use $g(x)=(x-1)^2+2$ since $0\leq3<4$

$$\begin{align*} g(3)&=(3-1)^2+2\\ &=2^2+2\\ &=4+2\\ &=6 \end{align*}$$

Step3: Calculate $f(2)+g(3)$

Add the two results

$$\begin{align*} f(2)+g(3)&=9+6\\ &=15 \end{align*}$$

Answer:

A. $9$
B. $6$
C. $15$