Answer
$(f\circ f)(4)=1$
Work Step by Step
$\bf{\text{Solution Outline:}}$
To evaluate the given expression, $
(f\circ f)(4)
,$ use the definition of function composition. Use the given table for the values of the function.
$\bf{\text{Solution Details:}}$
Since $(f\circ g)(x)=f(g(x)),$ then
\begin{array}{l}\require{cancel}
(f\circ f)(4)=f(f(4))
.\end{array}
Based on the table, the value of $
f
$ when $x=
4
$ is $
3
.$ Hence, $
f(4)=3
.$ By substitution, the equation above becomes
\begin{array}{l}\require{cancel}
(f\circ f)(4)=f(f(4))
\\\\
(f\circ f)(4)=f(3)
.\end{array}
Based on the table, the value of $
f
$ when $x=
3
$ is $
1
.$ Hence, $
f(3)=1
.$ By substitution, the equation above becomes
\begin{array}{l}\require{cancel}
(f\circ f)(4)=f(f(4))
\\\\
(f\circ f)(4)=1
.\end{array}