Since \(f\) is continuous, you know that
\(\displaystyle\lim_{x\to3}f(x)=f(3)=5\)
So,
\(\displaystyle\lim_{x\to3}(2f(x)-g(x))=2f(3)-\lim_{x\to3}g(x)=10-g(3)=4\)
where the limit for \(g\) also is equal to the value of \(g(3)\) because \(g\) is also continuous. This means \(g(3)=6\).
