Question

find $f(g(5))$ in simplified form.

$g(x)$ is a graph of a line. $h(x) = 3x^2 - 5x - 1$

$x$	$f(x)$
$-5$	$-9$
$-10$	$-4$
$3$	$4$
$9$	$8$

Explanation:

Step1: Find the equation of \( g(x) \)

The graph of \( g(x) \) is a straight line. Let's find its slope \( m \) and y-intercept \( b \). From the graph, when \( x = 0 \), \( y=-2 \), so \( b = -2 \). To find the slope, we can use two points. Let's take \( (0, -2) \) and \( (2, 0) \). The slope \( m=\frac{0 - (-2)}{2 - 0}=\frac{2}{2} = 1 \). So the equation of \( g(x) \) is \( g(x)=x - 2 \).

Step2: Calculate \( g(5) \)

Substitute \( x = 5 \) into \( g(x)=x - 2 \). So \( g(5)=5 - 2=3 \).

Step3: Calculate \( f(g(5))=f(3) \)

From the table of \( f(x) \), when \( x = 3 \), \( f(3)=4 \).

Answer:

\( 4 \)