Answer
$(f+g)(1)=8$
Work Step by Step
$\bf{\text{Solution Outline:}}$
To find the value of the given expression, $
(f+g)(1)
,$ use the definition of the appropriate function operation. Then substitute the values in the given table.
$\bf{\text{Solution Details:}}$
Using $(f+g)(x)=f(x)+g(x),$ then
\begin{array}{l}\require{cancel}
(f+g)(1)=f(1)+g(1)
\text{ (Equation *)}
.\end{array}
Based on the given table, when $x=
1
,$ the value of $f(x)$ is $
7
.$ Hence, $
f(1)=7
.$
Based on the given table, when $x=
1
,$ the value of $g(x)$ is $
1
.$ Hence, $
g(1)=1
.$
By substitution, Equation * becomes
\begin{array}{l}\require{cancel}
(f+g)(1)=f(1)+g(1)
\\\\
(f+g)(1)=7+1
\\\\
(f+g)(1)=8
.\end{array}