+322
Suppose f and g are continuous functions such that
g(9) = 6 and lim x → 9 [3f(x) + f(x)g(x)] = 27.
Find f(9).
+6251 \(\lim \limits_{x \to 9} \left(3f(x) + f(x)g(x)\right) = 27\\ 3 \lim \limits_{x \to 9} f(x) + \lim \limits_{x \to 9} f(x)g(x) = 27\\ 3 \lim \limits_{x \to 9} f(x) + g(9) \lim \limits_{x \to 9} f(x) = 27\\ 3 \lim \limits_{x \to 9} f(x) +6 \lim \limits_{x \to 9} f(x) = 27\\ 9 \lim \limits_{x \to 9} f(x) = 27\\ \lim \limits_{x \to 9} f(x) = 3 \\ f \text{ is given to be continuous so }\\ f(9) = \lim \limits_{x \to 9} f(x) = 3\)
.+6251 \(\lim \limits_{x \to 9} \left(3f(x) + f(x)g(x)\right) = 27\\ 3 \lim \limits_{x \to 9} f(x) + \lim \limits_{x \to 9} f(x)g(x) = 27\\ 3 \lim \limits_{x \to 9} f(x) + g(9) \lim \limits_{x \to 9} f(x) = 27\\ 3 \lim \limits_{x \to 9} f(x) +6 \lim \limits_{x \to 9} f(x) = 27\\ 9 \lim \limits_{x \to 9} f(x) = 27\\ \lim \limits_{x \to 9} f(x) = 3 \\ f \text{ is given to be continuous so }\\ f(9) = \lim \limits_{x \to 9} f(x) = 3\)
