Since g(6)=6, and both functions are continuous, we have:
[tex]\lim_{x \to 6} [3f(x)+f(x)g(x)] = 45\\\\\lim_{x \to 6} [3f(x)+6f(x)] = 45\\\\lim_{x \to 6} [9f(x)] = 45\\\\9\cdot lim_{x \to 6} f(x) = 45\\\\lim_{x \to 6} f(x)=5[/tex]
if a function is continuous at a point c, then [tex]lim_{x \to c} f(x)=f(c)[/tex],
that is, in a c ∈ a continuous interval, f(c) and the limit of f as x approaches c are the same.
Thus, since [tex]lim_{x \to 6} f(x)=5[/tex], f(6) = 5
Answer: 5
