Question

If f and g are continuous functions with f(3)=5 and lim x-->3 [2f(x)-g(x)]= 4, find g(3)

Answer 1

Because $f,g$ are continuous,

$\displaystyle\lim_{x\to3}(2f(x)-g(x))=2\lim_{x\to3}f(x)-\lim_{x\to3}g(x)=2f(3)-g(3)=4$
$10-g(3)=4$
$g(3)=6$