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# If $f(x)=x+7\: and \: g(x)=x-7, x \in R$ find fog(7).

Toolbox:
• Given two functions $f:A \to B$ and $g:B \to C$, then composition of $f$ and $g$, $gof:A \to C$ by $gof (x)=g(f(x))\;for\; all \;x \in A$
• Given two functions $g:A \to B$ and $f:B \to C$, then composition of $g$ and $g$, $fog:A \to C$ by $fog (x)=f(g(x))\;for\; all \;x \in A$
Given : $f(x)=x+7$
$g(x)=x-7$
$\therefore$ fog=$(x-7)+7$
$\Rightarrow x$
$fog(7)=7$