Question

two piecewise functions are shown below.
$h(x)=\

$$\begin{cases}-3x & \\text{for } x < 2 \\\\ 4x + 1 & \\text{for } x \\geq 2 \\end{cases}$$

$
$g(x)=\

$$\begin{cases}x^2 + 2 & \\text{for } x < 3 \\\\ x^3 & \\text{for } x \\geq 3 \\end{cases}$$

$
what is the value of $3h(2) + 4g(1)$?
a 39
b 28
c 10
d -8
8.
given $f(x) = 2x^2 - 3x + 1$ and $g(x) = 4x - 5$, find $f(2) + g(2)$.
a. 4
b. 6
c. 11
d. 24
9.
two piecewise functions are shown below.
$f(x)=\

$$\begin{cases}3x - 4 & \\text{for } x \\leq 5 \\\\ 2 - x & \\text{for } x > 5 \\end{cases}$$

$
$g(x)=\

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

$
what is the value of $4f(5) + 2g(3)$?
a 10
b 17
c 54
d 60
10.
a function is shown below.
$h(x)=\

$$\begin{cases}-\\frac{1}{2}x - 15 & \\text{for } x \\leq -4 \\\\ 20 - 3x^2 & \\text{for } x > -4 \\end{cases}$$

$
what is the value of $h(-4) + 3h(-2)$?

Explanation:

Problem 8

Step1: Calculate \( f(2) \)

Substitute \( x = 2 \) into \( f(x)=2x^{2}-3x + 1 \):
\( f(2)=2(2)^{2}-3(2)+1=2\times4 - 6 + 1=8 - 6 + 1 = 3 \)

Step2: Calculate \( g(2) \)

Substitute \( x = 2 \) into \( g(x)=4x - 5 \):
\( g(2)=4(2)-5 = 8 - 5 = 3 \)

Step3: Calculate \( f(2)+g(2) \)

Add the results: \( 3 + 3 = 6 \)

Step1: Calculate \( f(5) \)

Since \( 5\leq5 \), use \( f(x)=3x - 4 \):
\( f(5)=3(5)-4 = 15 - 4 = 11 \)

Step2: Calculate \( g(3) \)

Since \( 3\geq3 \), use \( g(x)=5 \):
\( g(3)=5 \)

Step3: Calculate \( 4f(5)+2g(3) \)

Substitute values: \( 4\times11+2\times5 = 44 + 10 = 54 \)

Step1: Calculate \( h(-4) \)

Since \( -4\leq - 4 \), use \( h(x)=-\frac{1}{2}x - 15 \):
\( h(-4)=-\frac{1}{2}(-4)-15 = 2 - 15=-13 \)

Step2: Calculate \( h(-2) \)

Since \( -2 > - 4 \), use \( h(x)=20 - 3x^{2} \):
\( h(-2)=20 - 3(-2)^{2}=20 - 3\times4 = 20 - 12 = 8 \)

Step3: Calculate \( h(-4)+3h(-2) \)

Substitute values: \( -13+3\times8=-13 + 24 = 11 \)

Answer:

b. 6

Problem 9