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 (9).,

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