Answer
\[f(2)=4\]
Work Step by Step
Given that $g(2)=6$
\[\lim_{x\rightarrow 2}[3f(x)+f(x)g(x)=36\]
\[\lim_{x\rightarrow 2}(3f(x))+\lim_{x\rightarrow 2}[f(x)g(x)]=36\]
\[3\lim_{x\rightarrow 2}f(x)+[\lim_{x\rightarrow 2}f(x)][\lim_{x\rightarrow 2}g(x)]=36\]
Since $f$ and $g$ are continuous
\[\Rightarrow 3f(2)+f(2)g(2)=36\]
\[\Rightarrow 3f(2)+6f(2)=36\Rightarrow 9f(2)=36\Rightarrow f(2)=4\]
Hence $f(2)=4$.
