Question

Suppose f and g are continuous functions such that g(6) = 6 and lim x → 6 [3f(x) + f(x)g(x)] = 45. Find f(6).

Answer 1

If a function is continuous, then \(\lim\limits_{x\to a}f(x)=f(a)\)

So, by the limit laws and by continuity:
\[\lim_{x\to6} \left[3f(x)+f(x)g(x)\right]=3f(6)+f(6)g(6)=45\] and \(g(6)=6\), so you just have one unknown to solve for, \(f(6)\) :)