Answer
$(g\circ f)(3)=9$
Work Step by Step
$\bf{\text{Solution Outline:}}$
To evaluate the given expression, $
(g\circ f)(3)
,$ 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}
(g\circ f)(3)=g(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}
(g\circ f)(3)=g(f(3))
\\\\
(g\circ f)(3)=g(1)
.\end{array}
Based on the table, the value of $
g
$ when $x=
1
$ is $
9
.$ Hence, $
g(1)=9
.$ By substitution, the equation above becomes
\begin{array}{l}\require{cancel}
(g\circ f)(3)=g(f(3))
\\\\
(g\circ f)(3)=g(1)
\\\\
(g\circ f)(3)=9
.\end{array}