دامنهٔ $:f + g$

$\eqalign{
  & Df = \left( {1\,,\,4} \right]  \cr 
  & {D_g} = \left[ {0\,,\,3} \right)  \cr 
  &  \Rightarrow {D_{f + g}} = {D_f} \cap {D_g} = \left( {1\,,\,4} \right] \cap \left[ {0\,,\,3} \right) = (1\,,\,3) \cr} $

ضابطهٔ $:f + g$

$g:\left\{ \begin{gathered}
  A(0\,,\,0) \hfill \cr 
  B(3\,,\,1) \hfill \cr 
 \end{gathered}  \right. \Rightarrow m = \frac{{{y_2} - {y_1}}}{{{x_2} - {x_1}}} = \frac{{1 - 0}}{{3 - 0}} = \frac{1}{3}$
$ \Rightarrow y - {y_1} = (x - {x_1}) \Rightarrow y = \frac{1}{3}x$
$ \Rightarrow g(x) = \frac{1}{3}x$
$f:\left\{ \begin{gathered}
  C(1\,,\,2) \hfill \cr 
  D(4\,,\,0) \hfill \cr 
 \end{gathered}  \right. \Rightarrow m = \frac{{{y_2} - {y_1}}}{{{x_2} - {x_1}}} = \frac{{0 - 2}}{{4 - 1}} =  - \frac{2}{3}$
$ \Rightarrow y - {y_1} = m(x - {x_1}) \Rightarrow y - 0 =  - \frac{2}{3}(x - 4)$
$ \Rightarrow f(x) =  - \frac{2}{3}x + \frac{8}{3}$
$(f + g)(x) = f(x) + g(x) = \frac{1}{3}x + \frac{8}{3} =  - \frac{1}{3}x + \frac{8}{3}$

نمودار $:f + g$

$(f + g)(x) =  - \frac{1}{3} + \frac{8}{3}$