Question

use the graphs to evaluate the expressions below.
$f(g(5)) = \square$
$g(f(2)) = \square$
$f(f(4)) = \square$
$g(g(1)) = \square$

Explanation:

Step1: Find g(5) from g(x) graph

From the graph of $g(x)$, when $x=5$, $g(5)=2$.

Step2: Find f(g(5))=f(2)

From the graph of $f(x)$, when $x=2$, $f(2)=3$.

Step3: Find f(2) from f(x) graph

From the graph of $f(x)$, when $x=2$, $f(2)=3$.

Step4: Find g(f(2))=g(3)

From the graph of $g(x)$, when $x=3$, $g(3)=3$.

Step5: Find f(4) from f(x) graph

From the graph of $f(x)$, when $x=4$, $f(4)=0$.

Step6: Find f(f(4))=f(0)

From the graph of $f(x)$, when $x=0$, $f(0)=5$.

Step7: Find g(1) from g(x) graph

From the graph of $g(x)$, when $x=1$, $g(1)=1$.

Step8: Find g(g(1))=g(1)

From the graph of $g(x)$, when $x=1$, $g(1)=1$.

Answer:

$f(g(5)) = 3$
$g(f(2)) = 3$
$f(f(4)) = 5$
$g(g(1)) = 1$