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).

Since g(6)=6, and both functions are continuous, we have:



if a function is continuous at a point c, then , 

that is, in a    c ∈  a continuous interval, f(c) and the limit of f as x approaches c are the same.

Thus, since , f(6) = 5

5