اگر $f(x)=۳x+a$ و $g(x)=۲-x$ و $۶=(x)(gof)-(x)(fog)$ باشد مقدار $a$ چقدر است؟
$\begin{align} & f(x)=3x+a\,\,\,\,,\,\,\,\,\,g(x)=2-x \\ & \left. \begin{matrix} (fog)(x)=f(g(x))=3g(x)+a=3(2-x)+a=6-3x+a \\ (gof)(x)=g(f(x))=2-f(x)=2-(3x+a)=2-3x-a \\\end{matrix} \right\} \\ & \Rightarrow (fog)(x)-(gof)(x)=(6-3x+a)-(2-3x-a) \\ & =4+2a\Rightarrow 4+2a=6\Rightarrow 2a=2\Rightarrow a=1 \\ \end{align}$