Question

homework assignment 1.4: composition of functions
score: 6/11 answered: 6/11
question 8
use the graphs to evaluate the expressions below.
graphs of f(x) and g(x) are provided (with x - axis from -1 to 6 and y - axis from -1 to 6).
$f(g(4)) = $
$g(f(3)) = $
$f(f(2)) = $
$g(g(0)) = $
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Explanation:

For \( f(g(4)) \):

Step1: Find \( g(4) \) from \( g(x) \) graph.

Looking at the graph of \( g(x) \), when \( x = 4 \), \( g(4)=3 \).

Step2: Find \( f(3) \) from \( f(x) \) graph.

Looking at the graph of \( f(x) \), when \( x = 3 \), \( f(3)=4 \). So \( f(g(4)) = 4 \).

For \( g(f(3)) \):

Step1: Find \( f(3) \) from \( f(x) \) graph.

From \( f(x) \) graph, \( f(3)=4 \).

Step2: Find \( g(4) \) from \( g(x) \) graph.

From \( g(x) \) graph, \( g(4)=3 \). So \( g(f(3)) = 3 \).

For \( f(f(2)) \):

Step1: Find \( f(2) \) from \( f(x) \) graph.

From \( f(x) \) graph, \( f(2)=5 \).

Step2: Find \( f(5) \) from \( f(x) \) graph.

From \( f(x) \) graph, when \( x = 5 \), \( f(5)=1 \). So \( f(f(2)) = 1 \).

For \( g(g(0)) \):

Step1: Find \( g(0) \) from \( g(x) \) graph.

From \( g(x) \) graph, \( g(0)=0 \).

Step2: Find \( g(0) \) from \( g(x) \) graph (again).

From \( g(x) \) graph, \( g(0)=0 \). So \( g(g(0)) = 0 \).

Answer:

s:
\( f(g(4)) = \boldsymbol{4} \)
\( g(f(3)) = \boldsymbol{3} \)
\( f(f(2)) = \boldsymbol{1} \)
\( g(g(0)) = \boldsymbol{0} \)