Question

use the graphs to evaluate the expressions below.
$f(g(3)) = \square$
$g(f(4)) = \square$
$f(f(1)) = \square$
$g(g(0)) = \square$

Explanation:

Step1: Find g(3) from graph

From the graph of $g(x)$, when $x=3$, $g(3)=4$.

Step2: Find f(g(3))=f(4)

From the graph of $f(x)$, when $x=4$, $f(4)=4$. So $f(g(3))=4$.

Step3: Find f(4) from graph

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

Step4: Find g(f(4))=g(4)

From the graph of $g(x)$, when $x=4$, $g(4)=5$. So $g(f(4))=5$.

Step5: Find f(1) from graph

From the graph of $f(x)$, when $x=1$, $f(1)=3$.

Step6: Find f(f(1))=f(3)

From the graph of $f(x)$, when $x=3$, $f(3)=4$. So $f(f(1))=4$.

Step7: Find g(0) from graph

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

Step8: Find g(g(0))=g(0)

From the graph of $g(x)$, when $x=0$, $g(0)=0$. So $g(g(0))=0$.

Answer:

$f(g(3)) = 4$
$g(f(4)) = 5$
$f(f(1)) = 4$
$g(g(0)) = 0$