Question

Suppose f and g are continuous functions such that

g(9) = 2
and
lim
x → 9
[3f(x) + f(x)g(x)] = 10.
Find
f(9)

Answer 1

`\bf \lim\limits_(x\to 9)\ 3f(x)+f(x)g(x)\quad =\quad 10 \\ \quad \\\\ \lim\limits_(x\to 9)\ 3f(9)+f(9)\underline{g(9)}=10\qquad \qquad \underline{g(9)}=2\qquad thus \\ \quad \\\\ 3f(9)+f(9)+f(9)2=10\implies 3f(9)+2f(9)=10`

solve for f(9)