## College Algebra (11th Edition)

$(f\circ g)(2)=1$
$\bf{\text{Solution Outline:}}$ To evaluate the given expression, $(f\circ g)(2) ,$ 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 g)(2)=f(g(2)) .\end{array} Based on the table, the value of $g$ when $x= 2$ is $3 .$ Hence, $g(2)=3 .$ By substitution, the equation above becomes \begin{array}{l}\require{cancel} (f\circ g)(2)=f(g(2)) \\\\ (f\circ g)(2)=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 g)(2)=f(g(2)) \\\\ (f\circ g)(2)=f(3) \\\\ (f\circ g)(2)=1 .\end{array}