Answer
$(f-g)(4)=21$
Work Step by Step
$\bf{\text{Solution Outline:}}$
To evaluate the given expression, $
(f-g)(4)
,$ given
\begin{array}{l}\require{cancel}
f(x)=x^2+3
\\
g(x)=-2x+6
,\end{array}
use the definition of the appropriate function operation. Then substitute $x$ with $
4
.$
$\bf{\text{Solution Details:}}$
Since $(f-g)(x)=f(x)-g(x),$ then
\begin{array}{l}\require{cancel}
(f-g)(x)=(x^2+3)-(-2x+6)
\\\\
(f-g)(x)=x^2+3+2x-6
\\\\
(f-g)(x)=x^2+2x-3
.\end{array}
Substituting $x$ with $
4
,$ then
\begin{array}{l}\require{cancel}
(f-g)(4)=(4)^2+2(4)-3
\\\\
(f-g)(4)=16+8-3
\\\\
(f-g)(4)=21
.\end{array}
