Suppose f and g are continuous functions such that g(9) = 5 and lim x → 9 [3f(x) + f(x)g(x)] = 24. find f(

F(9) = 3

For this problem, since we've been told that f and g are continuous, we know that they have defined values at x = 9. And since we've been given g(9) = 5, we can substitute the value 5 for every occurrence of g(9) in the given expression. So let's solve the expression to find f(9).
3f(x) + f(x)g(x) = 24
3f(9) + f(9)g(9) = 24
3f(9) + f(9)5 = 24
3f(9) + 5f(9) = 24
(3 + 5)f(9) = 24
8f(9) = 24
f(9) = 3