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

Since $f$ is continuous, you know that

$\displaystyle\lim_{x\to3}f(x)=f(3)=5$

So,

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

where the limit for $g$ also is equal to the value of $g(3)$ because $g$ is also continuous. This means $g(3)=6$.